annual report 03-04 - centre de recherches mathématiques

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Contents

PRESENTING THE ANNUAL REPORT 2003-2004 1

SCIENTIFIC PROGRAMS 2003-2004 2

Theme Year 2003-2004: Geometric and Spectral Analysis 2

Past Thematic Programs 10

Aisenstadt Chairholders in 2003-2004: S.T. Yau and P. Sarnak 11

General Program 2003-2004 13

Interdisciplinary and Industrial Program 16

Joint Institute Initiatives 17

CRM Prizes 20

CRM-ISM Colloquium Series 25

CRM PARTNERS 27

INDUSTRIAL COLLABORATIONS 29

RESEARCH LABORATORIES 30

CICMA 30

CIRGET 32

Mathematical Analysis laboratory 35

LaCIM 38

Applied Mathematics Laboratory 41

Mathematical Physics Laboratory 43

Statistics Laboratory 45

PhysNum 48

PUBLICATIONS 51

Recent Titles 51

Previous Titles 51

Preprints and Research Reports 55

SCIENTIFIC PERSONNEL 58

Long-term visitors 58

Short-term visitors 59

Postdoctoral Fellows 60

CRM Members in 2003-2004 61

TWO COMMITTEES HEADING THE CRM 64

Bureau de direction 64

Scientific Advisory Commitee 65

PERSONNEL 2003-2004 67

STATEMENT OF REVENUE AND EXPENDITURES 68

MISSION OF THE CRM 70

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eport presenting by the Director

Presenting the annual report 2003-2004

François Lalonde, Director of CRM

The 2003-2004 year, thinking particularly about the thematic program in Geometric and Spectral Analysis, was certainly one of the greatest theme years ever organized by the CRM. It was a veritable firework of activi-ties, discoveries, and unexpected collaborations; a year orchestrat-ed with great intelligence and in-sight by Jacques Hurtubise who was able to bring about the con-centrated state of effervescence

and dynamism that characterizes moments of great discoveries. That year was supervised by CRM Acting Director, my colleague Christian Léger, to whom we owe a great deal: he combined a rigorous administration, giving generously of his time with great devotion and attention to details. The CRM hosted over 1750 participants and visitors in 2003-2004 within the context of its thematic, general and industrial programs.

The thematic program drew over 500 participants, 15 long-term visitors and five year-long postdoctoral fellows. It included three mini-courses and two Aisenstadt Chair lecture series (given by S.T. Yau and Peter Sarnak), and especially a record number twelve workshops spread over the year, including one organized with AARMS (Atlantic Canada) and two with the Fields Insti-tute (Toronto) as part of their thematic program in Partial Dif-ferential Equations. The last issue of the Bulletin du CRM(Fall 2004) published a superb retrospective of the year written by Iosif Polterovich. The year was organized by Bierstone, Craig, Finster, Jakobson, Jaksic, Kamran, Last, Melrose, Milman, Pil-let, Phong, Polterovich, Toth and Zelditch.

The general program (which is non-thematic) was not outdone. It hosted a Workshop on Algebraic Structures and Moduli Spac-es organized by Markman and Nakajima, the 61st Colloque des Sciences mathématiques du Québec held in April 2004 at CRM,

and A Workshop on Graph Theory in honour of Bondy and Fleischner in May 2004. The industrial and multidisciplinary program was plentiful with eleven workshops and events orga-nized in collaboration with MITACS, ncm2, CIRANO, IEEE, IFM, GERAD and SSC One of these, DeMoSTAFI (Depen-dence Modelling in Statistics and Finance) resulted in special issues in two journals: the Canadian Journal of Statisticsand In-surance: Mathematics and Economics, the journal of reference in actuarial science.

The eight research laboratories (thematic research groups) of the CRM, having just completed a year of existence, organized a very nice conference in honour of Paul Koosis on Classical Analysis (see the article in the Fall 2004 issue of Bulletin du CRM), a CICMA Workshop on Computational Perspectives on L-Functions and p-adic Cohomology organized by Darmon and Pila, a Workshop on Functional Data Analysis organized by Léger in Ramsay (Statistics Laboratory), the Montreal Scien-tific Computing Days now a well-established tradition thanks to Bourlioux and Gander of the Applied Mathematics Labora-tory, and a Workshop on Tau Functions organized by CIRGET. These laboratories are a remarkable achievement:some existed for a number of years thanks to the foresight of FCAR in fi-nancing research teams (be they specialized or multidisciplinary) with its infrastructure grants program of the 1990s. Thanks to ISM, ten now well-established scientific groups have seen the light of day in the last decade. The CRM’s laboratories have per-mitted a further advance by offering secure funding and a more direct access to the CRM’s infrastructure to these groups. It has resulted in a more acute sense of collegiality and community, which has given a fresh impetus to mathematical research. These eight laboratories supported by CRM are the source of the most fruitful initiatives; it is in them that the CRM draws its resources and its originality. Thanks to them and the devoted members of the Scientific Advisory Committee, the programs of the CRM, which was one the first two or three centres in the world to see the value of thematic synergy, remain a prime worldwide ex-ample in this domain.

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The core of each year’s scientific program at the CRM is its thematic program. The Scientific Advisory Committee chose for 2003-2004 the theme of Geometric and Spectral Analysis because of its importance, timeliness and impact on the interna-tional scientific community. The thematic program included several workshops and conferences, two Aisenstadt Chair lecture series (Yau and Sarnak), a number of visiting scientists in residence, and some postdoctoral fellowships. In coordination with Montréal universities, CRM offers appropriate short courses in order to help graduate students participate in the activities. The reports are presented in the language in which they were submitted.

OverviewAnalysis has traditionally stood at the center of a wide spectrum of research activities in mathematics. In particular, the fields of geometric and spectral analysis have played a fundamental role in shaping the major themes of current research in differ-ential geometry and math-ematical physics, and now touch in an important way onto areas such as number theory and algebraic geom-etry. They are at the core of several of the deepest and most spectacular advances in these fields. The thematic year in geometric and spectral analysis focussed focus on a number of themes in which this interaction has been particularly fruitful. The year is organized around two intercon-nected themes: the first, whose different subthemes cover the whole year, is principally centered on various questions in spec-tral analysis; it comprises a short programme on analysis on sin-

gular spaces, and a more extended period on spectral analysis in geometry, mathematical physics and number theory. The second theme relates to the analysis of the Einstein equations, a subject on which there has been spectacular progress in recent years. It

is concentrated in the fall of 2003. These themes have been cho-sen for a balance between the geometric and spectral components of the scientific

programme, and also with the objective of highlighting some of the most interesting current applications of analytic ideas to physics. There was be a strong emphasis on training through the short courses which preceded the proposed workshops, as well as through the coordination of the graduate course offerings in analysis and geometry in the Montreal universities.

Theme Year 2003-2004: Geometric and Spectral Analysis

Scientific Programs 2003-2004

In particular, the fields of geometric and spectral analysis have played a fundamental role in shaping the major themes of current research in differential geometry and mathematical physics, and now touch in an important way onto areas such as number theory and algebraic geometry.

Organizing Commitee

E. Bierstone (Toronto), W. Craig (McMaster), F. Finster (Regensburg), D. Jakobson (McGill), V. Jaksic (McGill), N. Kamran (McGill), Y. Last (Hebrew), R. Melrose (MIT), P. Milman (Toronto), C. Pillet (Toulouse), D.H. Phong (Columbia), I. Polterovich (Montréal), J. Toth (McGill), S. Zelditch (Johns Hopkins).

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rogramation 2003-2004

Aisenstadt Chair Lecture Series: Yau & Sarnak

As always, among the highlights of the year were the lectures given by the Aisenstadt Chairs. The first series of the Aisenstadt lectures was delivered by Shing-Tung Yau (Harvard). He gave a broad survey of the analytical problems that arise in the study of isolated systems in general relativity, culminating with a fas-cinating new definition of quasi-local mass recently discovered together with his student Melissa Liu (Ph.D. 2002, Harvard). The positivity properties of this mass were developed in detail. Professor Yau’s lectures were part of the Workshop on the Inter-action of Gravity with Classical Fields, organized by Felix Fin-ster (Regensburg) and Niky Kamran (McGill). This workshop was preceded by another one, devoted to the Cauchy problem for the Einstein equations, also organized by Finster and Ka-mran. The Riemannian Penrose inequality, the conformal Ein-stein equations and the nonlinear stability of Minkowski space were among the topics covered during this event.

The other series of the Aisenstadt lectures was given by Peter Sarnak (NYU and Princeton) at the Workshop on Spectral The-ory and Automorphic Forms, organized by Dmitry Jakobson (McGill) and Yiannis Petridis (CUNY). Professor Sarnak gave a general introduction on the spectrum of the modular group, followed by a discussion of the latest research on the relation between quantum and classical fluctuations. His last lecture on lattice packings in higher dimensions was based on a joint work with Andreas Strömbergsson (Ph.D. 2001, Uppsala). One of the recent breakthroughs in the field was E. Lindenstrauss’s proof of the Rudnick-Sarnak quantum unique ergodicity conjecture for arithmetic surfaces. Lior Silberman (Ph.D. student, Princeton) and Akshay Venkatesh (Ph.D. 2002, Princeton) reported on their extension of this proof to locally symmetric spaces.

Short programme on analysis and resolution of singularities

August 18-September 5, 2003

Org.: E. Bierstone (Toronto), R. Melrose (MIT), P. Milman (Toronto), D.H.

Phong (Columbia).

Speakers: Janusz Adamus (Toronto), Jochen Brüning (Humboldt), Sagun

Chanillo (Rutgers), Xiuxiong Chen (Wisconsin-Madison), Michael

Christ (Berkeley), Andrew Comech (Duke), John P. D’Angelo (Illinois,

Urbana-Champaign), Klas Diederich (Wuppertal), Lawrence Ein (Illinois

at Chicago), Charles Louis Fefferman (Princeton), Akito Futaki (Tokyo,

Inst. of Technology), Caroline Grant Melles (US Naval Academy), Michael

Greenblatt (Wisconsin-Madison), Allan Greenleaf (Rochester), Daniel Grieser

(Bonn), Eugénie Hunsicker (Lawrence), Jacques Hurtubise (McGill), Niky

Kamran (McGill), Robert Lazarsfeld (Michigan), Ben Lichtin (Rochester),

John Loftin (Columbia), Zhiqin Lu (UC Irvine), Toshiki Mabuchi (Osaka),

George Marinescu (Humboldt), Rafe Mazzeo (Stanford), Mircea Mustata

(Clay Mathematics Inst.), Andreea C. Nicoara (Harvard), Takeo Ohsawa

(Nagoya), Wieslaw Pawlucki (Jagiellonian), Markus Pflaum (Johann

Wolfgang Goethe-Univ.), Malabika Pramanik (Wisconsin-Madison), Leslie

D. Saper (Duke), Yum-Tong Siu (Harvard), Karen E. Smith (Michigan),

Jian Song (Columbia), Jacob Sturm (Rutgers), S. Tankeev (Vladimir State

Technical Univ.), John A. Toth (McGill), Alexander Varchenko (North

Carolina at Chapel Hill), Sophia Vassiliadou (Georgetown), Stephen Wainger

(Wisconsin-Madison), Ben Weinkove (Columbia), Jaroslaw Wlodarczyk

(Purdue), James Wright (Edinburgh), Jared Wunsch (Northwestern) Chan

Woo Yang (Johns Hopkins), Maciek Zworski (Berkeley).

Number of participants: 62

The Short Program on Analysis and Resolution of Singularities was the first major activity in CRM’s Thematic Year on Ge-ometry and Spectral Theory. The Short Program was unique in bringing together researchers in algebraic geometry, complex differential geometry and partial differential equations. It was organized in three separate weeks:

1. Workshop on oscillatory integrals and critical inte-grability exponents

The topics included degeneracy of holomorphic functions in several variables, Tian-Yau invariants of complex manifolds, de-generate Fourier integral operators and Legendre distributions, multiplier ideal sheaves and jet schemes.

2. Short courses

Three mini-series of four lectures each, accessible to graduate students: Resolution of singularities (from an analyst’s point of view), E. Bierstone (Toronto), Singularities in harmonic and geo-metric analysis, D.H. Phong (Columbia), and Metrics, fibrations and singular spaces, R. Melrose (M.I.T.).

3. Workshop on resolution of singularities, metrics and the Laplacian

The workshop was directed towards the differential topology of, and differential analysis on, singular spaces, especially algebraic varieties. The general problem of the appropriate definition of the Laplacian, and correspondingly harmonic forms, was exten-sively discussed with emphasis on unresolved questions concern-ing the domain of the Laplacian and the regularity and structure of Hodge and weighted deRham forms.

A particular focus was a description of harmonic forms on sin-gular projective varieties via an understanding of the structure of the Fubini-Study metric lifted to a resolution.

The program was particularly successful in bringing together not only researchers in different mathematical areas, but also leading experts, students and postdocs. The large number of younger participants reflected the great current interest of the main top-ics. Several of the speakers in each workshop were postdoctoral fellows.

The program was organized to stimulate progress on problems in geometric and harmonic analysis that had led to the first inter-actions between multiplier ideal sheaves and partial differential equations in complex geometry, between resolution of singulari-ties and oscillatory integrals, and between desingularization of the Fubini-Study metric and harmonic analysis on singular spac-

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es. It was highly successful – researchers in these areas were able to get first-hand insight into each other’s work, and advances on the main problems began even during the meeting. (For exam-ple, a problem discussed by Melrose on desingularization of the Fubini-Study metric can be solved in the case of toric varieties using a combinatorial desingularization algorithm of Bierstone-Milman discussed also during the second week.)

Workshop on the Cauchy problem for the Einstein equations

September 24-28, 2003

Org.: F. Finster (Regensburg), N. Kamran (McGill)

Speakers: Abhay Ashtekar (Pennsylvania State), Adrian Butscher (Toronto),

Matthew W. Choptuik (UBC), Piotr Chrusciel (Tours), Helmut Friedrich

(Max-Planck-Institut), Greg Galloway (Miami), Gerhard Huisken (Max-

Planck-Institut), James Isenberg (Oregon), Jerzy Kijowski (Center for

Theoretical Physics), Jerzy Lewandowski (Warszawski), Ezra T. Newman

(Pittsburgh), Francesco Nicolo (Roma “Tor Vergata”), Daniel Pollack

(Washington), Harald Schmid (Regensburg).


This workshop brought together some of the world’s leading ex-perts in the study of the Cauchy problem for the Einstein field equations of general relativity. This is a question of paramount physical importance in trying to understand the formation of singularities and black holes. It is also an extraordinary challenge for mathematicians interested in non-linear hyperbolic and par-abolic partial differential equations.

The workshop opened with four extremely useful introductory lectures by Abhay Ashtekar and Gerhard Huisken, who reviewed the geometric, analytic and physical foundations of the problem, including the positivity of mass, the asymptotic structure at spa-tial and null infinity and the Penrose inequality. These introduc-tory lectures were followed by more specialized lectures covering the proof of the Riemannian Penrose inequality by Bray and Huisken/Ilmanen, the stunning results of Christodoulou on the cosmic censorship conjecture for spherically symmetric gravi-tational fields, the proof by Klainerman-Nicolo of the global non-linear stability of Minkowski space-time using double null foliations, the new formulation of the conformal Einstein equa-tions by Helmut Friedrich, the smoothness problem for confor-mal infinity by Piotr Chrusciel, and the search for the optimal Sobolev exponent ( how to get from 5/2 to 2 ? ) by Klainerman and Rodnianski. Jim Isenberg gave a marvelous lecture entitled “what we know and don’t know about the constraint equations” which was a tour-de-force of synthesis and exposition. Overall, there was an extraordinary sense of continuity in the lectures, which were an extremely stimulating experience for the students and experts alike.

Workshop on the interaction of gravity with classical fields

October 1-5, 2003

Org.: F. Finster (Regensburg), N. Kamran (McGill).

Speakers: Stephen Anco (Brock), Håkan Andreasson (Chalmers Univ. of

Technology), Brandon Carter (LUTH, Observatoire de Paris-Meudon),

Mihalis Dafermos (MIT), Peter Forgacs (Tours), Hiroko Koyama (National

Astronomical Observatory), Jutta Kunz (Oldenburg), Hans-Peter Kunzle

(Alberta), Alexander Linden (Canberra), Dieter Maison (Max Planck

Institut), Raymond G. McLenaghan (Waterloo), Éric Poisson (Guelph),

Antonio Sa Barreto (Purdue), Harald Schmid (Regensburg), Avy Soffer

(Rutgers), John Stalker (Princeton), Bernard Whiting (Florida), Shing-Tung

Yau (Harvard).


The interaction of gravity with classical fields leads quickly to some very deep questions of physical and analytical interest, such as the possible absence of space-time singularities when gravity is coupled to a non-Abelian gauge field or a fermion field, or the linear stability of rotating black holes. Indeed, Birkhoff’s theorem asserts that pure gravity does not exhibit any dynamical behavior, so that the presence of non-trivial dynamics requires that gravity be coupled to a matter field.

The remarkable and totally unexpected discovery through nu-merical methods by Bartnik and McKinnon of the existence of everywhere regular, localized solutions of the Einstein Yang-Mills equations, and the subsequent proof by Finster, Smoller and Yau of the existence of stable regular localized spherically symmetric solutions of the Einstein Yang-Mills equations gave a tremendous impetus to the area, where the non-linear inter-action of gravity with repulsive forces is surprisingly seen to give rise to stable solutions for certain ranges of the coupling constants. The workshop brought together some of the world’s leading players in the subject and was held in conjunction with Shing-Tung Yau’s Aisenstadt lectures on mathematical analysis in general relativity.

Again, there were opening lectures on the foundations of the subject, given by P. Forgacs and H. Kunzle. The highlights of the lecures included a talk by Mihalis Dafermos on his stun-ning proof of Price’s law for the decay of scalar fields coupled to gravity, lectures by Dieter Maison on “colored black holes”, Avy Soffer on decay of non-linear waves in Schwarzschild geom-etry, Brandon Carter on gravitating branes, Hakan Andreasson on the existence of solutions to the Einstein Vlasov system, and Felix Finster on wave equations in the Kerr metric. One of the hopes that emerged as a result of this workshop is that a proof of the linear stability of the Kerr black hole for perturbations in-volving infinitely many modes may be within reach. This would have been unlikely even ten years ago.

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Workshop on large N limits of U(N) gauge theory in physics and mathematics

January 5-9, 2004

Org.: P. Bleher (IUPUI), V. Kazakov (École Normale) et S. Zelditch (Johns

Hopkins)

Speakers: Marco Bertola (Concordia), Michael Douglas (Rutgers), Charlie

Frohma (Iowa), William M. Goldman, (Maryland), Alice Guionnet (ENS

de Lyon), John Harnad (Concordia), Dmitry Korotkin (Concordia), Ivan

Kostov (SPHT Saclay), Andrei Okounkov (Princeton), Nicolai Reshetikhin

(Berkeley), Mariya Shcherbina (Ukrainian Ac. Sci.), Matthias Staudacher

(Albert-Einstein-Institut), Richard Wentworth (Johns Hopkins), Christopher

Woodward (Rutgers), Ofer Zeitouni (Minnesota).


The topic of this workshop, held during the winter of 2004 at the Centre de recherches mathématiques, was the large N limit of Yang-Mills theory in dimension 2 and in related large N limits of matrix models. The subject was born in the observation of Gerard ‘t Hooft in 1972 that only planar Feynman diagrams survive the large N limit. This seems to indicate that the large N lim-it of gauge theory is a string theory. To a mathematician, this means that integrals over moduli spaces of U(N) bundles over a Riemann surface have an asymptotic expansion in powers of N involving branched covers of the Riemann surface. Precise conjectures were formulated in the early 90’s by D. J. Gross, W. Taylor, V. Kazakov, M. Douglas, G. Moore and others, largely based on exact formulae for the partition function by A. Migdal.

The workshop opened with a long talk by V. Kazakov on the background of the conjectures and some recent physical devel-opments related to them. M. Douglas then lectured on his ideas relating large N limits to conformal field theories. For many in the audience, these talks were the foundations for their future discussions with the physicists. I. Kostov, and M. Staudacher gave more specialized talks on matrix models and gauge theories in the large N limit.

On the second day, N. Reshetikhin described his work with A. Okounkov and others on 3D Young diagrams, a kind of 3D ana-logue of the 2D large N limits. A. Okounkov then explained the background representation theory and probabililty theory. These lectures were masterful in their grasp of both the physical theories and the rigorous results related to them. S. Zelditch then present-ed rigorous results on the large N limits of partition functions and characters which contradicted the conjectures of D.J. Gross- A. Matytsin and of V. Kazakov-T. Wynter. Members of the au-dience suggested several explanations (not all consistent) on how to fix the conjectures. Later that day, C. Frohman explained an approach to the calculation of expected values of Wilson loop functionals and polynomials in Wilson loops, based on a dia-grammatic approach to knots and links.

The third day was devoted to large deviations and statistical

mechanics. A. Guionnet and O. Zeitouni explained how large deviations theory proved the conjectures of Gross-Matytsin on spherical integrals and characters, once they were analytically con-tinued to positive matrices. These positive results contrasted the counterexamples of Zelditch for large N asymptotics of characters on U(N). Clearly, the conjectures were false in the oscillating re-gime and correct in the positive regime. Guionnet also explained relations to free probability which in principal ‘solve’ all random matrix models in the large N limit. P. Bleher surveyed his work on random matrix models. In the afternoon, M. Shcherbina ex-plained her proof of the Douglas-Kazakov phase transition and also her results on spectral statistics of random matrix models. J. Harnad presented his results on random matrix models and biorthogonal polynomials. These were later followed by talks by his collaborators, Korotkin and Bertola on asymptotics of parti-tion functions of matrix models.

The fourth day was largely devoted to the geometry of gauge theories. W. Goldman and R. Wentworth explained the Morse theory of the Yang-Mills functional. That led to C. Wood-ward’s rigorous proof of the Migdal formula, based on a sum over critical points of the YM functional. Goldman’s talk also provided background for the talk of F. Labourie on his im-portant recent results on large N limits of moduli spaces of SL(N, R) connections. His limit space bore an intriguing rela-tion to the conformal field theory conjectured by M. Douglas many years ago, and it will be interesting to understand the rela-tion further.

The audience was quite eclectic, ranging from physicists to an-alysts to probabalists to geometers to representation theorists. Nevertheless, the participants affirmed frequently and spontane-ously that there was much fruitful discussion across boundar-ies. Certain members of the audience, e.g. A. Okounkov and M. Douglas, had a sure grasp of virtually every aspect of the conference and were very helpful in gluing together the dispa-rate groups. For instance, A. Guionnet and O. Zeitouni could rigorously explain the ‘saddle-point’ arguments of the physicists from the viewpoint of large deviations, and A. Okounkov could explain the representation theory behind their views on large N limits.

Thus, in four short days, the conference succeeded in tying to-gether numerous fuzzy threads in the literature and a variety of new project were born. For further details concerning the workshop, please log on the web site at www.crm.umontreal.ca/Gauge/

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Workshop on spectral geometry

March 4-6, 2004

Org.: Iosif Polterovich (Montréal)

Speakers: Mark S. Ashbaugh (Missouri), Jean-Marc Bouclet (Lille 1),

Maxim Braverman (Northeastern), Jochen Brüning (Humboldt), Zindine

Djadli (Cergy-Pontoise), Leonid Friedlander (Arizona), Dmitri Gioev

(Pennsylvania), Carolyn S. Gordon (Dartmouth College), Michael Hitrik

(UCLA), Victor Ivrii (Toronto), Eran Makover (Connecticut College), Dan

Mangoubi (Technion), Rafe Mazzeo (Stanford), Peter A. Perry (Kentucky),

Steve Zelditch (Johns Hopkins).


Posing the right question is sometimes more important in math-ematics than finding the answer. It has been almost forty years since Mark Kac asked “Can one hear the shape of a drum?’’, but the study of the interplay between the geometry and the spectrum remains as active as ever. Some recent developments in this field were discussed at the Workshop on Spectral Geometry, organized by Iosif Polterovich (Montréal).

AARMS-CRM - Workshop on singular integrals and analysis on CR manifolds

May 3-8, 2004, Halifax, Nova Scotia

Org.: Galia Dafni (Concordia), Andrea Fraser (Dalhousie)

Speakers: Shiferaw Berhanu (Temple), Albert Boggess (Texas A&M), Der-

Chen Chang (Georgetown), Paulo Ciatti (Padova), Anthony Dooley (New

South Wales), Wayne Eby (Temple), Gerald Folland (Washington), Simon

Gindikin (Rutgers), Peter C. Greiner (Toronto), Jennifer Lynn Halfpap

(Wisconsin- Madison), Adam Koranyi (CUNY Lehman College), Alexander

Nagel (Wisconsin-Madison), Maria Roginskaya (Chalmers), Linda Rothschild

(UC San Diego), Nancy Stanton (Notre Dame), Wolfgang Staubach (Fields),

Keith F. Taylor (Dalhousie), Jingzhi Tie (Georgia), Dimiter Vassilev (CRM),

James Wright (Edinburgh), Jie Xiao (Memorial).


The theory of singular integral operators in the context of analysis on CR submanifolds of Cn, in particular the Heisenberg group, has been studied and proven fruitful over the last 30 years. In recent years, the emphasis has shifted to singular integral opera-tors which do not fall under the standard Calderon-Zygmund theory. These include operators arising from product kernels on nilpotent Lie groups, which in turn lead to the study of flag kernels. The workshop brought together researchers from the areas of harmonic analysis, several complex variables, symmetric spaces and Lie groups.

The centerpiece of the conference was a series of five lectures de-livered by Alexander Nagel (Wisconsin-Madison) and outlining his recent fundamental work on the following topics: the theory of product singular integrals on products of Carnot-Carathe-odory spaces, flag kernels on homogeneous nilpotent Lie groups and applications to quadratic CR manifolds (joint with Fulvio Ricci and Elias M. Stein), the d-bar-b complex on decoupled domains (joint with Elias M. Stein), and the Bergman kernel for the “cross of iron” domain (joint with Malabika Pramanik).

The rest of the talks in the workshop concerned results that touched on these various topics and related subjects. Many par-ticipants commented on the fact that the conference was very focused and the speakers were all interested in each other’s talks. The half-hour talks by younger participants were also very ap-preciated and allowed the senior mathematicians to see what the new generation of mathematicians is working on. The atmo-sphere during the workshop was very convivial.

Workshop on spectral theory and automorphic forms

May 4-7, 2004

Org.: D. Jakobson (McGill), Y. Petridis (The Graduate Center and Lehman

College, City University of New York))

Speakers: Andrew Booker (Paris-Sud), Gautam Chinta (Brown), Alina

Carmen Cojocaru (Princeton), Eduardo Duenez (Johns Hopkins), Alexander

Gamburd (Stanford), Dorian Goldfeld (Columbia), Gergely Harcos (Texas

at Austin), Dennis A. Hejhal (Minnesota and Uppsala), Harald Helfgott

(Yale), Lizhen Ji (Michigan), Chris Judge (Indiana), Habiba Kadiri (CRM),

Emmanuel Kowalski (Bordeaux I), Jens Marklof (Bristol), Stephen David

Miller (Rutgers), Steven J. Miller (Ohio State), Werner Müller (Bonn), Ram

Murty (Queen’s), Cormac O’Sullivan (CUNY), Peter A. Perry (Kentucky),

Andrei Reznikov (Weizmann Institute of Science), Guillaume Ricotta

(Montpellier), Zeev Rudnick (Tel-Aviv), Peter Sarnak (Princeton), Richard

Sharp (Manchester), Lior Silberman (Princeton), Morten Skarsholm Risager

(Aarhus), Kannan Soundararajan (Michigan), Fredrik Stromberg (Uppsala),

Akshay Venkatesh (MIT).


The Conference coincided with the three lectures of Peter Sar-nak, Chair Aisenstadt 2003-2004. While the first lecture was a general introduction on the Spectrum of the modular group, the subsequent lectures discussed latest results on quantum and clas-sical fluctuations and lattice packing.

The participants included 10 of his 34 students. The overall level of the activity was extremely high. A number of the participants have been recently awarded various distinctions, e.g. A. Cojoca-ru and Nathan Ng have been awarded the Doctoral Prize of the Canadian Math Society (2003, 2001), K. Soundararajan is a Sa-lem Prize Winner (2004), S. D. Miller is a Sloan Fellow (2003), A. Venkatesh is a Clay Research Fellow (2004), Z. Rudnick won the Erdos Prize 2001, R. Murty won the Jeffery-Williams prize 2003 and the Queen’s Research Prize 2003.

Topics debated were ranging from the computational aspects of Maass cusp forms to subconvexity problems for L-functions with applications to Quantum Ergodicity and Quantum Chaos, the problem of existence of cusp forms and Weyl’s Law, relations with dynamical systems and arithmetic, statistical behavior of zeros of L-functions and relation to the Riemann Hypothesis, multiple Dirichlet series etc.

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Workshop on Integrable and Near-integrable Hamiltonian PDE

May 17-21, 2004

Org.: W. Craig (McMaster), P. Deift (Courant Inst.), S. Kuksin (Heriot-

Watt), P. Olver (Minnesota), J. Toth (McGill), P. Winternitz (Montréal).

Speakers: Simonetta Abenda (Bologna), Dario Bambusi (Milano),

Massimiliano Berti (SISSA, Trieste), Roy Choudhury (Central Florida),

Percy Deift (CIMS), Hakan Eliasson (Paris VII), Benoît Grébert (Nantes),

John Harnad (CRM & Concordia), Eduard-Wilhelm Kirr (Chicago), Sergei

Kuksin (Heriot-Watt), Nader Masmoudi (CIMS), Maung Minoo (McMaster),

N. Sri Namachchivaya (Illinois at Urbana-Champaign), Jürgen Pöschel

(Stuttgart), David Sattinger (Yale), Michael Sigal (Notre Dame & Toronto),

Vladimir Sokolov (Landau Institute), Jacek Szmigielski (Saskatchewan),

Alexander Tovbis (Central Florida), Eugene Wayne (Boston), Stephanos

Venakides (Duke), Vitali Vougalter (McMaster), Doug Wright (McMaster),

Yingfei Yi (Georgia Institute of Technology), Jiangong You (Nanjing), Xin

Zhou (Duke).

Among the topics that were discussed at the workshop were: KAM theory for PDE and other Hamiltonian systems possessing infinitly many degrees of freedom, Nekhoroshev stability theory and analogs of Arnold diffusion in infinite dimensional systems, extension of techniques of quadrature for integrable systems, in-cluding elements of inverse spectral theory and random matrix theory, and refined asymptotics of integrable systems in singular limits such as the small dispersion limit. This workshop was a part of the Fields Institute’s year long program on partial dif-ferential equations, as well as being a cooperative effort with the CRM special year on Spectral analysis and geometry.

Workshop on Hamiltonian Dynamical systems (jointly with the Fields Institute)

May 24-28, 2004

Org.: Dario Bambusi (Milano), Walter Craig (McMaster), Sergei B. Kuksin

(Heriot-Watt), C. Eugene Wayne, Chair (Boston) & Eduard Zehnder (ETH,

Zurich).

Speakers: S. Bolotin (Wisconsin), C.-Q. Cheng (Nanjing), L. Chierchia (Roma

Tre), R. de la Llave (Texas at Austin), D. Gaidashev (Toronto), V. Gelfreich

(Warwick), G. Gentile (Roma Tre), V. Ginzburg (UC at Santa Cruz), D.

Gomes (Berkeley), H. Hofer (Courant Institute), L. Jonsson (Fields Institute),

T. Kappeler (Institut für Mathematik, Zürich), D. Khmelev (Toronto), M.

Levi (Penn State), J. Mather (Princeton), K. Meyer (Cincinnati), D. Offin

(Queen’s), D. Sauzin (CNRS - Institut de Mécanique Céleste), L. Stolovitch

(CNRS-Laboratoire Emile Picard), D. Treschev (Moscow State University),

M. Yampolsky (Toronto), C. Zeng (Virginia).


This workshop focused on analytic techniques of Hamiltonian dynamical systems, including perturbation theory, variational methods and stability theory. The subject includes both finite dimensional Hamiltonian systems such as in celestial mechan-ics, and infinite dimensional Hamiltonian systems, such as those arising from PDE or from other dynamical systems with infi-nitely many degrees of freedom.

This meeting was in fact a continuation of a regular series of workshops on analytic methods for Hamiltonian dynamical sys-tems. This series was an outgrowth of the famous Oberwolfach workshops organized by J. Moser and E. Zehnder. The last two workshops took place at the International Centre for Mathemat-ical Sciences in Edinburgh, at two year intervals of time. Funding for these meetings has come from from the European Community, the EPSRC of Britain, the NSF Committee for In-ternational Programs, the Clay Mathematics Institute. The sup-port for the CRM/Fields workshop on Hamiltonian dynamical systems comed from the NSERC, the Fields Institute, the CRM and the Canada Research Chairs Program.

In particular, we planned a schedule similar to prior meetings, with only four to six talks per day which left plenty of time for interactions between the participants and informal discussions. Among the topics that were discussed at the workshop were drift and diffusion in Hamiltonian systems, KAM theory, applica-tions of symplectic geometry to Hamiltonian dynamics and ce-lestial mechanics.

A particular focus was the phenomenon of Arnold diffusion in which arbitrarily small perturbations of integrable Hamiltonian systems may result in instability of the system’s trajectories. First described exactly 40 years ago by V.I. Arnold (Instability of dy-namical systems with many degrees of freedom, Dokl. Akad. Nauk SSSR 156 1964) this phenomenon was understood for many years only in the context of certain special examples. In the last five or six years, however, a number of different approaches have begun to yield a more complete understanding of this ba-sic property of Hamiltonian dynamics and many of the talks at this workshop were devoted to explicating the geometrical, variational and perturbative techniques that are needed to un-ravel this phenomenon. As its name suggests, there is a certain randomness in the trajectories that are observed in systems un-dergoing Arnold diffusion and some of the talks also discussed this relationship between the apparent unpredictability of these randommotions and the determinism inherent in classical me-chanical systems.

Another topic figuring in several talks was celestial mechanics. It was the study of planetary motion that led to the creation of Hamiltonian dynamics and the subject remains a source of in-teresting problems for the field. The talks on celestial mechanics ranged from the study of quasi-periodic motions in the solar sys-tem to studies of integral manifolds in the three-body problem; the techniques brought to bear on their solution, which ranged from the very analytical approach of the Kolmogorov-Arnold-Moser Theory to a topological investigation of the energy sur-faces, illustrated how broad the mathematical underpinnings of Hamiltonian dynamics have become.

The mechanics of the workshop exhibited the close cooperation of the Fields Institute and the Centre de Recherches Mathé-matiques.Montréal was an ideal locale for the meeting, and we think that the CRM and the city made a lasting good impression on the workshop participants.

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Workshop on semi-classical theory of eigenfunctions and PDEs

June 1-11, 2004

Org.: D. Jakobson (McGill), J. Toth (McGill)

Speakers: Ivana Alexandrova (California, Berkeley), Alex Barnett (Courant

Institute), Marco Bertola (Concordia), Xu Bin (Tokyo Institute of

Technology), Eugène Bogomolny (Paris-Sud), David Borthwick (Emory),

Alain Bourget (McGill), Nicolas Burq (Paris-Sud), Yves Colin de Verdière

(Grenoble I), Walter Craig (McMaster), Harold Donnelly (Purdue), Cristian

Enache (Laval), Leonid Friedlander (Arizona), Patrick Gerard (Paris-Sud),

Daniel Grieser (Bonn), Pengfei Guan (McMaster), Victor Guillemin (MIT),

Eric Heller (Harvard), Luc Hillairet (École Normale Supérieure de Lyon), Alex

Iantchenko (Malmö), Alexandru Ionescu (Wisconsin Madison), Victor Ivrii

(Toronto), Chris Judge (Indiana), Shannon Lee Starr (CRM), Maung Min-Oo

(McMaster), Nikolai Nadirashvili (Chicago), Fedor Nazarov (Michigan State),

Yiannis N. Petridis (City Univ. of New York Lehman College), Vesselin Petkov

(Bordeaux 1), Georgi Popov (Nantes), Yuri Safarov (King’s College London),

Mikhail Shubin (Northeastern), Alexander Sobolev (Sussex), Christopher

Sogge (Johns Hopkins), Alexander Stohmaier (Bonn), Tatsuya Tate (Keio),

Alejandro Uribe (Michigan), Andre Voros (CEA), Andre Voros (CEA-CENS),

Steve Zelditch (Johns Hopkins), Maciek Zworski (Berkeley).


The correspondence principle in quantum mechanics predicts that the behaviour of the high-energy eigenfunctions reflects the properties of the corresponding classical system – the geodesic flow. This was the central theme of the Workshop on Semi-Clas-sical Theory of Eigenfunctions and PDEs, organized by Dmitry Jakobson and John Toth (McGill). In particular, the workshop focused on the phenomena of “scarring”: exceptional localiza-tion of the eigenfunctions around the periodic orbits of the clas-sical flow. Scarring was the topic of the lectures of the physicists Eugene Bogomolny (Orsay) and Eric Heller (Harvard). Profes-sor Heller, among other things, demonstrated that eigenfunc-tions belong not only to science, but also to art! His exhibition “Visions from the quantum frontier,’’ presented at the Centre d’exposition de l’Université de Montréal, featured a beautiful “portrait gallery” of eigenfunctions, created using numerical simulations of various quantum systems.

Workshop on spectral theory of Schrödinger operators

July 26-30, 2004

Org.: V. Jaksic (McGill), Y. Last (Hebrew)

Speakers: Michael Aizenman (Princeton), Joseph Avron, Jean-Marie

Barbaroux (Centre de Physique Théorique), Jonathan Breuer (Hebrew), Jean

Michel Combes (Centre de physique théorique), Ovidiu Costin (Rutgers ),

Rafael del Rio (UNAM), Alexander Elgart (Stanford), Alexander Fedotov

(Institute of Physics), Alexander Figotin (UC Irvine), Richard G. Froese

(UBC), François Germinet (Cergy-Pontoise), Peter Hislop (Kentucky), Dirk

Hundertmark (Illinois at Urbana-Champaign), Svetlana Jitomirskaya (UC

Irvine), Alain Joye (Institut Fourier, Grenoble), Yulia Karpeshina (Alabama

at Birmingham), Rowan Killip (UCLA), Werner Kirsch (Ruhr-Univ.

Bochum), Alexander Kiselev (Wisconsin Madison), Abel Klein (UC Irvine),

Frédéric Klopp (UMR – CRNSG), Ari Laptev (Royal Institute of Technology,

Stockholm), Daniel Lenz (TU Chemnitz), Peter Mueller (Goettingen),

Yehuda Pinchover (Technion-Israel Institute of Technology), Joaquim

Puig (Barcelona), Oleg Safronov (Alabama at Birmingham), Barry Simon

(Caltech), Alexander Sobolev (Sussex), Peter Stollmann (TU Chemnitz),

Gunter Stolz (Alabama at Birmingham), Yosef Strauss (Hebrew), Serguei

Tcheremchantsev (Orléans), Boris Vainberg (UNC-Charlotte).


The focus of this workshop was spectral theory of random and quasiperiodic Schrodinger operators. In solid state phys-ics these operators serve as models of disordered systems, such as alloys, glasses and amorphous materials. The disorder of the system is reflected by the dependence of the potential on some random parameters.

The workshop has brought together the world leaders in spec-tral theory of random and quasi-periodic operators. The mini-courses were given by M. Aizenman (Princeton), who spoke on spin-glass systems and recent spectacular resolution of Pa-risi conjecture by Talagrand, by B. Simon (Caltech), who spoke on the spectral theory of orthogonal polynomials, and S. Jitomirskaya (Irvine), who spoke on the recent spectacular resolution of the final part of the celebrated Mark Kac “Ten Martini Problem”. The resolution of the “Ten Martini Prob-lem” took over two decades, and practically all major contrib-utors were in the audience. After Jitomirskaya’s lecture, M. Aizenman, the editor of “Communications in Mathematical Physics,” has awarded silver olives to the present contribu-tors.

The workshop had a heavy schedule---besides three two-hours mini-courses, there were thirty two half hour lectures. The quality of the talks, the attendance and the atmosphere were extraordinary.

A particularly noticeble was a number of young people---start-ing with Joaquim Puiq, who was then still a graduate student (and who completed the “Ten Martini Problem”) and ending with a number of first year graduate students who got their first exposition to the field on this conference.

The general feeling among senior participants about the con-ference was very positive. A number of them thought that in the terms of the scientific impact and quality of the organiza-tion this was the best conferences in spectral theory of Schro-dinger operators in the last twenty years.

Workshop on dynamics in statistical mechanics

August 2-6, 2004

Org.: V. Jaksic (McGill), C.-A. Pillet (Toulon)

Speakers: H. Araki (Kyoto), J. Bellissard (Atlanta), P. Blanchard

(Bielefeld), L. Bruneau (Warsaw), T. Chen (Courant), S. De Bievre (Lille),

J. Derezinski (Warsaw), B. Derrida (Paris), J.-P. Eckmann (Geneva), G.

Elliott (Toronto), A.C. D van Enter (Groningen), L. Erdös (Münich),

B. Helffer (Paris), G-M. Graf (ETH), M. Griesemer (Alabama), C. Jäkel

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(Münich), G. Jona-Lasinio (Rome), A. Knauf (Erlangen), R. Livi (Florence),

M. Merkli (Montreal), T. Matsui (Kyushu), B. Nachtergaele (Davies),

K. Netocny (Groningen), F. Nier (Rennes), Y. Ogata (Tokyo), Y. Pautrat

(Montreal), L. Rey-Bellet (Amherst), R. Seiringer (Princeton), D. Spehner

(Essen), S. Starr (Montreal), L. Thomas (Virginia), A. Verbeure (Leuven),

H.T. Yau (Stanford), L.-S. Young (Courant), V. Zagrebnov (Marseille).


This workshop was devoted to the study of dynamical proper-ties of (classical and quantum) open systems with particular em-phasis on the recent developments in non-equilibrium statistical mechanics. In recent years, through the study of noisy or forced dissipative systems, or Hamiltonian systems with a large number of degrees of freedom, our understanding of the mathematical structure of nonequilibrium statistical mechanics has greatly improved. The aim of this meeting was to present the latest re-sults and discuss the possible future directions of research in this area.

The mini-courses were given by B. Derrida (École Normale), who gave an introduction to surprising new variational prin-ciples in classical non-equilibrium statistical mechanics (these results were further elaborated in the talk of G. Jona-Lasinio), by H. Araki (Kyoto), who reviewed the recent work on Gibbs variational principle for interacting quantum fermionic systems, by J-P. Eckmann (Geneva), who spoke on the fundamental open problem of derivation of macroscopic Fourier law for heat conductance from microscopic Hamiltonian dynamics (and its resolution for a toy model of Eckmann-Young), and by L. Er-dos (Munich), who spoke on spectacular recent progress in the study of hydrodynamical limits.

An important aspect of the conference was the variety of top-ics covered, all of which had a relation (sometimes surprising) with the main theme. For example, F. Nier’s talk on semiclas-sical analysis of low-lying eigenvalues of Witten Laplacians was closely related to the study of non-equilibrium steady states of classical open system by Eckmann-Pillet-Bellet. The other topics ranged from spin systems (Matsui, Nachtergaele, Starr) to quan-tum field theory (Derezinski, Jakel, Bruneau).

The Friday afternoon section was devoted to talks of young re-searchers (mainly postodcs)--Bruneau, Merkli, Ogata (who was still a graduate student), Pautrat and Netocny. These talks con-firmed that the future of this difficult and fundamental field, which goes back to fundamental work of Bolzmann and Gibbs, and which still causes sometimes the contraversies in scientfific circles, is in good hands.

Compared with recent major workshop at CIRM, Marseille (held in March 2003), practically all participants were surprised how many novel results have been obtained in a short span of one year and a half.

The field of non-equilibrium statistical mechanics has staged a spectacular progress in the last decade, and this workshop was a very important snapshot of its development. Just like the CIRM

workshop, we are confident that the CRM workshop will also lead to major new developements. We expect to see some of them at the next major workshop---a two month (Jan-March 2005) program on “Open Systems” in “Schrodinger Institute” in Vienna (organized by Derezinski, Graf, Yngvanson).

Exposition Heller

À l’occasion du 125e anniversaire de l’Université de Montréal, le CRM a présenté, du 13 mai au 1er juin 2004, une exposition d’une trentaine d’oeuvres d’Eric J. Heller au Centre d’exposition de l’Université. Cette exposition, qui s’intitulait « Aux confins de l’univers quantique », fut également présentée pendant quelques semaines au Centre des sciences du Vieux-Port de Montréal.

Le professeur Heller, qui partage son temps entre les Départements de physique et de chimie de l’Université Harvard, étudie le monde quantique des molécules, des atomes et des électrons en effectuant des simulations numériques sur ordinateur. Depuis le milieu des années 80, il crée des oeuvres d’art à partir de graphiques tirés de ces simulations. Ses oeuvres, qui évoquent les mystères de l’univers quantique, ont vite connu une très vaste diffusion tant dans les centres d’exposition que dans la presse.

Deux conférences publiques soulignèrent cette exposition. Le 13 mai, Jean LeTourneux, directeur adjoint du CRM, parla de « La science derrière les oeuvres d’Eric Heller », et le 1er juin, le professeur Heller, après avoir prononcé la conférence d’ouverture de l’atelier sur la théorie semi-classique des fonctions propres et équations aux dérivées partielles, présenta au Centre d’exposition un exposé intitulé « Art, Science and Politics ».

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Past Thematic ProgramsThe Centre de recherches mathématiques has organized thematic activities every year since 1993. Before that, starting in 1987, special semesters and concentration periods were combined with thematic years. Here follows a list of thematic activities organized by CRM since 1987:

2002-2003 Math in Computer Science

2001-2002 Groups and Geometry

2000-2001 Mathematical Methods in Biology and Medicine

1999-2000 Mathematical Physics

1998-1999 Number Theory and Arithmetic Geometry

1997-1998 Statistics

1996-1997 Combinatorics and Group Theory

1995-1996 Applied and Numerical Analysis

1994-1995 Geometry and Topology

1993-1994 Dynamical Systems and Applications

1992 Probability and Stochastic Control (special semester)

1991-1992 Automorphic Forms in Number Theory

1991 Operator Algebras (special semester)

1990 Nonlinear PDE’s and Applications (focal period)

1988 Shimura Varieties (special semester)

1987 Quantum Field Theory (special semester)

1987-1988 Fractals: Theory and application

1987 Structural Rigidity (special semester)

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Shing-Tung YauProfessor Yau obtained his Ph.D. in Mathematics from the Uni-versity of California at Berkeley in 1971, under Professor Chern’s supervision. After spending a year at the Institute for Advanced Study, he taught successively at S.U.N.Y. Stony Brook, at Stanford University, at the Institute for Advanced Study, at the University of California at San Diego, and at the University of Texas at Austin. In 1987 he was appointed Professor of Mathematics at Harvard University, a position he has held ever since.

Aisenstadt Chairholders in 2003-2004: S.T. Yau and P. Sarnak

The Aisenstadt Chair was endowed by Montréal philanthropist Dr. André Aisenstadt. Under its auspices, one or more dis-tinguished mathematicians are invited each year for a period of at least one week, ideally one or two months. During their stay the lecturers present a series of lectures on a specialized subject. They are also invited to prepare a monograph (see the Publications section in this report for a list of these publications). At the request of Dr. Aisenstadt, the first of their lectures should be accessible to a wide audience. Previous holders of the Aisenstadt Chair are: Marc Kac, Eduardo Zarantonello, Robert Hermann, Marcos Moshinsky, Sybren de Groot, Donald Knuth, Jacques-Louis Lions, R. Tyrell Rockafellar, Yuval Ne’eman, Gian-Carlo Rota, Laurent Schwartz, Gérard Debreu, Philip Holmes, Ronald Graham, Robert Langlands, Yuri Manin, Jerrold Marsden, Dan Voiculescu, James Arthur, Eugene B. Dynkin, David P. Ruelle, Robert Bryant, Blaine Law-son, Yves Meyer, Ioannis Karatzas, László Babai, Efim I. Zelmanov, Peter Hall, David Cox, Frans Oort, Joel S. Feldman, Roman Jackiw, Duong H. Phong, Michael S. Waterman, Arthur T. Winfree, Edward Frenkel, Laurent Lafforgue, George Lusztig, László Lovász and Endre Szemerédi.

His fields of research are differential geometry, differential equa-tions and general relativity. He has received the highest awards for his outstanding contributions. Besides the Fields Medal (1982), he was awarded the Veblen Prize (1981), the Carty Prize of the National Academy (1981), the Crafoord Prize of the Royal Swe-dish Academy(1994), and the National Medal of Science, U.S.A. (1997). In 1979, he was elected California Scientist of the year. He is a member of the American Academy of Arts and Sciences, ot the Chinese Academy of Sciences, of the Academia Sinica, and of the Russian Academy of Sciences. He has received four honorary doctorates and he is an honorary professor of many universities.

Professor Yau lecturing at CRM in October 2003..

Professor Yau with CRM Acting Director Christian Léger..

The CRM was honoured to have as Aisenstadt chairholders, during the 2003-2004 theme year Geometric and Spectral Analysis, Professors Shing-Tung Yau of Harvard University and Peter Sarnak of Courant Institute.

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Peter Sarnak

Professor Sarnak was born in Johannesburg, South Africa in 1953. He obtained his bachelors degree from University of Witwaters-rand in 1975 and his Ph.D. from Stanford University in 1980.

He joined the Courant Institute as an assistant professor in 1980, be-coming an associate professor in 1983. He moved to Stanford Uni-versity as a Professor in 1987. In 1989 he was the Sherman Fairchild Distinguished scholar at Caltech. Since 1991 he has been a professor of mathematics at Prin-ceton University. There

he was the H. Fine Professor from 1995-6, Department Chair from 1996-9 and since 2002 is the Eugene Higgins Professor of Mathematics. Between 1999 and 2002 he was a member of the Institute for Advanced Study at Princeton, and since 2001 he is also a Professor of Mathematics at the Courant Institute.

Professor Sarnak has received numerous awards and honours in-cluding being a Sloan Fellow (1983-5) and a Presidential Young Investigator (1985-90). He was awarded the Polya Prize by SIAM in 1998, the Ostrowski prize from the Ostrowski Foundation in 2001 and the Levi L. Conant Prize of AMS in 2003. He was elected to the American Academy of Arts and Sciences in 1991 and both as a member of the National Academy of Sciences (USA) and as a Fellow of the Royal Society (UK) in 2002.

He has published more than 90 academic journal papers, and writ-ten several books, and edited several more, as well as supervising more than thirty (thirty two at last count) PhD students.

His main interests are in the theory of zeta functions with appli-cations to number theory, mathematical physics and automorphic forms. His citation on election to the Royal Society states that he is ‘’distinguished for his major contributions to analysis and number theory. He is widely recognised internationally as one of the leading analytic number theorists of his generation. His early work on the existence of cusp forms led to the disproof of a con-jecture of Selberg. He has obtained the strongest known bounds towards the Ramanujan conjectures for sparse graphs and he was one of the first to exploit connections between certain questions in theoretical physics and analytic number theory.”

Chaire Aisenstadt - continued

Peter Sarnak.

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General Program 2003-2004The CRM’s general program funds a wide variety of scientific events, both on-site, elsewhere in Canada and around the world. Whether it be for specialized workshops for a small number of researchers, large meetings for hundreds of partici-pants or activities for high school or undergraduate students, the general program promotes research in the mathematical sciences at all levels. The program is quite flexible, allowing projects to be considered as they arise. The reports are presented in the language in which they were submitted.

Séminaire de Mathématiques Supérieures: Structural Theory of Automata, Semigroups, and Universal Algebra

July 7-18, 2003

Org.: Ivo Rosenberg, (Montréal), Valeriy Kudryavtsev, (Moscow State).

Speakers: Jorge Almeida (Porto), Joel Berman (Illinois at Chicago), Jürgen

Dassow (Magdeburg), Rusins Freivalds (Latvia), Andrei Krokhin (Warwick),

Alexander Letichevsky (Glushkov Institute of Cybernetics, NAS Kiev,

Ukraine), Ralph McKenzie (Vanderbilt), Ivo Rosenberg (Montréal), Lev

N. Shevrin (Ural State Univ.), Magnus Steinby (Turku), Mikhail Volkov

(Ural State Univ.).

The lectures at this NATO Advanced Study Institute covered a wide range of the theory of automata, semigroup theory and universal algebra. The topics of the lectures mostly related at least two of the three fields, used concepts and techniques from other domains and showed some intrinsic connections.

Structural theory of automata Two of the courses were concerned with problems arising from the construction – via composition and feedback – of new au-tomata from a given set of automata over the same input and output alphabets. A basic problem is to find a completeness criterion. In the feedback-free case, the question of uniformly delayed completeness, requiring complex universal algebra and relational tools, was addressed by Rosenberg. Variants of the general problem induced by certain equivalence relations were discussed by Dassow. A correspondence between varieties of finite algebras and varieties of tree languages was presented by Steinby. Finite quantum automata – a close counterpart of probabilistic finite automata – and the combinatorial problems related to recognizability of languages were presented by Freiv-alds. The behaviour of the general interaction of agents and environments were considered by Letichevsky.

SemigroupsThe lectures dealt with fundamental results often connected to the other two topics. Profinite semigroups, presented by Almeida, use algebraic and topological methods and serve for classifying rational languages. Automata, algorithmic and com-plexity-theoretical aspects of semigroup varieties (Volkov) relate semigroups and computer science. Epigroups, a large, rich and interesting class of semigroups, were presented by Shevrin.

Universal algebraAn important problem that appears in computer science, op-erations research, data bases and combinatorics is the so-called constraint satisfaction problem. An algebraic approach to it, based on clones and relations, and the computational complex-ity aspects, was presented by Krokhin. The sizes of finitely gen-erated free algebras in a locally finite variety form an important structural invariant of the variety. Their covers were discussed by Berman. Congruence modular varieties include groups, rings, modules and lattices. The commutator theory, a basic tool for the study of such varieties, was presented by McKenzie.

In addition to the main lecture series there were five one-hour presentations on topics related to the main lectures: varieties arising from finite languages, endoprimal algebras in certain varieties, syntactic congruences, topological quasivarieties, and counting problems for certain types of algebras.

Workshop on Algebraic Stuctures and Moduli Spaces

July 14-20, 2003

Org.: Eyal Markman (Massachusetts), Hiraku Nakajima (Kyoto).

Speakers: Claudio Bartocci (Univ. degli Studi di Genova), Alexander

Braverman (Harvard), Jim Bryan (UBC), Andrei Caldararu (Pennsylvania),

Linda Chen (Columbia), Mark de Cataldo (SUNY at Stony Brook), Kenji

Fukaya (Kyoto), Victor Ginzburg (Univ. of California at Santa Cruz), Jacques

Hurtubise (McGill), Hiroshi Iritani (Kyoto), Lisa Jeffrey (Toronto), Dmitry

Kaledin (Independent Univ. of Moscow), Manfred Lehn (Johannes Gutenberg

- Univ. Mainz), Yoshinori Namikawa (Kyoto), Keiji Oguiso (Tokyo), Justin

Sawon (SUNY at Stony Brook), Michael Thaddeus (Columbia), Ravi Vakil

(Stanford), Misha Verbitsky (Glasgow), Weiqiang Wang (Virginia), Kota

Yoshioka (Kobe).


One of the most fruitful interactions of modern mathematics has been the interplay between geometry and algebra; one sim-ply has to think of the role homogeneous spaces have played in illuminating and expanding various concepts of representation theory. Conversely, a good algebraic action is often the key to understanding the geometry and the topology of a geometrical object. This was the central theme of a conference on Algebraic Structures and Moduli Spaces held at the CRM from July 14-20, 2003.

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Hidden Algebraic StructureThe usefulness of uncovering “hidden” algebraic structure in the topology of various spaces is of course not new. An early manifestation of this was the Lefschetz decomposition theorem of Kähler geometry. A Kähler structure on a compact complex manifold is determined by a closed two-form on the manifold with certain properties. The operations of taking exterior prod-uct with this two form and of contracting by the same two-form define an action of the lie algebra of sl(2,C) on the harmonic forms on the manifold, and so on the cohomology. Decompos-ing the cohomology into irreducible representations gives a lot of information on the structure of the manifold. Another exam-ple of a truly intricate algebraic structure, of a more topological nature, has its origins in the study of the space Map*(Sn,X) of based maps from the n-sphere Sn into a space X. The space of maps is tied to configurations of points in the n-plane, and one obtains an intricate algebra of operations on the homology of this space in terms of natural operations on points in the plane. This algebraic structure and others like it were formalised into what is called an operad, and twenty years later, it was realised that this structure had important applications in the understand-ing of moduli spaces.

Fundamental ObjectsThese moduli spaces are fundamental objects in algebraic ge-ometry and differential geometry. They parametrise geometric objects of a given type; one speaks, for example, of the moduli space of curves, or the moduli space of holomorphic vector bun-dles on a manifold, or of the moduli of instantons on a four manifold. These spaces have a remarkably beautiful structure in their own right; they also yield deep and detailed information on the base space over which they are defined: for example, the instantons over a four-manifold Y are remarkably fine tools for studying Y, or the holomorphic and pseudo-holomorphic maps from a Riemann surface into a holomorphic or symplectic mani-fold Z give us detailed invariants of the structure. Moduli spaces also have a remarkable habit of popping up all over the place in physics, and physicists have been at the origin of an astounding variety of deep conjectures on these spaces.

Nakajima and Grojnowski discoveriesAt the conference, one example that was the subject of a beauti-ful four-hour series of talks by M. Lehn was the Hilbert scheme Hilbn(X) of n points on a complex surface X. This variety parametrises 0-dimensional subschemes of X of length n; the generic element of Hilbn(X) corresponds to n unordered distinct points of X; when the points collide, Hilbn(X) in some sense remembers some information about the way they did it. There are natural subvarieties of Hilbn(X)×X×Hilbm(X) which can be used to define operations on the cohomology of the union of these schemes; it was the discovery of Nakajima and Grojnowski that these operations define an action of an infinite dimensional Heisenberg algebra on the cohomology. An extension of this representation to a larger vertex algebra, explains much of the structure of the cohomology rings of the Hilbert schemes. This, and further developments, were explained by Lehn. In a sepa-rate lecture, W. Wang related the tau-function of the 2-Toda

hierarchy to a generating function, arising from the equivariant cohomology of Hilbert schemes of points in the affine plane.

Remarkable conjectures by NekrasovIn another vein, H. Nakajima and K. Yoshioka gave another very stimulating four hour series of talks on instanton counting on blow-ups. There are some remarkable conjectures by Nekrasov relating Seiberg-Witten prepotentials for supersymmetric gauge theories to integrals over the moduli space of instantons; the lec-turers explained their proof of this conjecture using the relations between torsion free sheaves on a blow-up of P2 and on P2. A. Braverman, later in the conference, gave his own constructions on a related moduli space, tying these integrals to intersection cohomology on a suitable compactification. The talks covered many aspects of the structure of moduli spaces and the invari-ants obtained from them: Gromov-Witten invariants and stable maps (J. Bryan, M. Thaddeus), Floer homology (K. Fukaya, H. Iritani), Hochshild cohomology and orbifold cohomology (A. Caldararu, L. Chen, D. Kaledin), Fourier-Mukai and Nahm-Fourier transforms (C. Bartocci, Y. Namikawa, J. Sawon), links to representation theory (V. Ginzburg, L. Jeffrey, R. Vakil). One of the basic cases for testing various aspects of the theory is the moduli space of K3 surfaces, and these surfaces were a substan-tial feature of several of the talks, notably those of K. Oguiso and M. Verbitski. The Lefschetz theorem, while several decades old, resurfaced in a recent version during the conference in a talk by M. de Cataldo. The workshop was held over a full week, with four hours of lectures per day and a long break at lunch for discussion. The fourth day was held at McGill’s Gault estate at Mont Saint-Hilaire, a beautiful forested location by a lake; after a morning session, the group adjourned for a walk in the woods. All made it back to the bus that afternoon, bringing with them, it is hoped, a few additional theorems. These, and an account of the talks at the conference, have appeared in CRM Proceedings and Lecture Notes.

61e Colloque des Sciences Mathématiques du Québec

April 24, 2004

Plenary Speakers: Fahima Nekka (Montréal), Jiri Patera (Montréal) and

Tom Ransford (Laval)


Quatre ateliers ont été organisés. En voici la liste ainsi que les conférenciers pertinents:

Physique MathématiqueOrg.: PiergiulioTempesta (CRM)

Speakers: Alexander Hariton (Montréal), Marco Merkli (McGill), Vasilia

Shramchenko (Concordia), Libor Snobl (CRM), Shannon Starr (CRM),

Piergiulio Tempesta (CRM).

AnalyseOrg.: Matthias Neufang (Carleton)

Speakers: Remus Floricel (Ottawa), Cristian Ivanescu (Toronto), Isidore

Fleischer (CRM), Benjamin Itza-Ortiz (Ottawa), Claus Koestler (Queens).

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AlgèbreOrg.: Ibrahim Assem (Sherbrooke)

Speakers: Jessica Lévesque (Sherbrooke), David Smith (Sherbrooke),

Jennifer Bélanger (Sherbrooke), Marcelo Lanzilotta (Republica), Julie

Dionne (Sherbrooke).

Communications libresOrg.: Alain Rémillard (Montréal

Speakers: Jacques Labelle (UQAM), Luc Bélair (UQAM), Michel Valley

(Laval), Constfantin Costara (Laval), Claudius Liviu Todor (Montréal).

Graphes et leurs cycles (Bondy et Fleischner ont 60 ans)

May 10-14, 2004

Org.: Gena Hahn (Montréal), Gert Sabidussi (Montréal)


Colloque en l’honneur des soixante ans de J. A. Bondy et H. Fleischner, spécialistes en théorie des graphes en général et de la problématique des cycles dans des graphes en particulier. Le livre de Bondy et Murty est un des plus utilisé pour enseigner la théorie des graphes.

Les organisateurs ont laissé beaucoup de temps pour des discus-sions, chose bien appréciée. En effet, beaucoup de participants ont exprimé à plusieurs reprises leur satisfaction du format et du contenu du colloque.

Les conférences étaient de très bon niveau et rendaient hommage aux travaux des deux invités d’honneur, comme la renommée in-ternationale de la majorité des conférenciers le laissait espérer.Le colloque était financé par des frais d’incription et soutenu par le CRM qui a fourni la salle de conférence, l’accès internet aux participants ainsi qu’un soutien matériel et qui a contribué aux frais de voyage de H. Fleischner.

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Interdisciplinary and Industrial Program

Summer School: The Mathematics of Bioinformatics

August 27-29, 2003, Univ. de Montréal

Org.: Nadia El-Mabrouk (Montréal), David Sankoff (Ottawa).

Speakers: Anne Bergeron (UQAM), Guillaume Bourque (CRM), David

Bryant (McGill), Miklós Csürös (Montréal), Nadia El-Mabrouk (Montréal),

Mike Hallett (McGill), Jotun Hein (Oxford), John Kececioglu (Arizona),

Mathieu Raffinot (Evry), David Sankoff (Ottawa).


L’objectif de cette école était d’introduire l’auditoire aux divers domaines de la bioinformatique, en favorisant des exposés péda-gogiques clairs, qui introduisent le domaine avant de rentrer dans des aspects de recherche plus pointus. Cet esprit a été parfaitement respecté. En 1h30, le présentateur avait le temps de faire une bonne introduction au domaine, avant de parler de ses recher-ches propres. Plusieurs retours positifs sur l’école ont été reçus, en particulier de la part de professeurs de divers départements et de diverses universités (Canada et États-Unis) qui souhaitaient initier des formations en bioinformatique dans leurs départements, et qui trouvaient, dans cette école, toute la matière pour monter un cours. À la suite d’un grand nombre de demandes, il a été décidé de rendre disponibles tous les documents pertinents et les présentations des chercheurs sur la page web de l’école.

Dependence Modeling: Statistical Theory and Applications in Finance and Insurance

May 20-22, 2004, Château Laurier, Québec

Org.: Michel Gendron (Laval), Christian Genest (Laval), Étienne Marceau

(Laval), Louis-Paul Rivest (Laval).

Speakers: B. C. Arnold (Riveside), M. Denuit (Univ. catholique de Louvain), P.

Embrechts (ETH Zürich), K. Ghoudi (United Arab Emirates), H. Joe (UBC),

É. Marceau (Laval), R. B. Nelsen (Lewis and Clark College), D. Oakes

(Rochester), M. Scarsini (Torino).

Supported by: CRM, MITACS, Institut de finance mathématique de

Montréal, Université Laval.


This international meeting was intended as a sequel to the series of conferences on copulas and their applications that were held in Rome (1990), Seattle (1993), Prague (1996) and Barcelona (2000). The meeting took place at the Château Laurier, near Québec City’s historical district, from Thursday, May 20, to Saturday, May 22, 2004.

As in previous editions, the meeting attracted copula specialists and statistical researchers interested in their development and use in characterizing and modeling dependence (stochastic orderings, distributions with fixed margins, etc.). As suggested by the title of the event, however, the meeting provided special emphasis on inferential aspects surrounding the use of copulas, and gave high visibility to their applications in actuarial science and finance.

Dependence issues and their treatment in survival analysis, ex-treme-value theory and hydrology were also central to the theme of the conference.

The keynote address, with historical overtones, was given by Prof. R. B. Nelsen, who is the author of a well known monograph on modeling dependence through copulas. Other plenary lectures were given by the invited speakers listed above. Each one, 45 minutes in length, surveyed major methodological developments on a specific aspect of the theory (concepts, methods, models, estimation, tests, etc.) and gave broad overviews of recent areas of application. Prof. Embrechts’ lecture, delivered on Friday mor-ning, was particularly lively and appreciated by the audience. Over 55 contributed talks, each 20 minutes in length, were also pre-sented by participants from 18 different countries. Contributors were affiliated mostly with universities and research institutes, but actuarial firms, banks, and government departments or agencies were also well represented in the audience.

The main highlight of the cultural program was a field trip to Montmorency falls, on late Friday afternoon. This was followed by a four-course dinner at the Manor, located at the top of the falls, and by an excellent introduction to French Canadian mu-sical traditions by renowned Quebec folk singer Yves Lambert and three musicians. Participants had plenty of opportunities to mingle at that event, as well as in between sessions or at night in parks, museums and restaurants located nearby the conference hotel, where nearly everyone stayed.

The conference was generally regarded as highly successful, both from a professional and a social perspective. Added visibility will be conferred to the event through the publication of peer-reviewed proceedings in the form of special issues of The Canadian Journal of Statistics/La revue canadienne de statistique (CJS) and Insu-rance: Mathematics and Economics (IME). In total, 29 manus-cripts were submitted to these two issues, currently expected to be published in June, 2005. The IME issue will be edited by C. Genest, with the help of the three other organizers listed above. Genest will also serve as Editor for the CJS issue, with his collea-gue L.-P. Rivest, as well as H. Joe (UBC) and HEC Professors D. Dupuis and B. Rémillard serving as Associate Editors.

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Joint Institute InitiativesCertain activities of Canadian societies in the mathematical sciences are jointly sponsored by the Fields Institute, the Centre de recherches mathématiques, the Pacific Institute for the Mathematical Sciences, and in some cases by MITACS.

CMS Summer Meeting 2003

June 14–16, 2003

University of Alberta

Meeting Director: YanPing Lin (Alberta).

The 2003 CMS Summer Meeting was held at the University of Alberta on June 14-16, 2003, and welcomed 348 participants. The meeting began with Robert Moody (Alberta) delivering a Public Lecture entitled Tilings: an evening excursion to the zoo. The event, held at the Telus Center, drew a large audience and was followed by a welcoming reception.

Other special events included plenary talks delivered by: Ingrid Daubechies (Princeton), Roland Glowinski (Houston), Gerhard Huisken (Tuebingen/Albert Einstein Institute), James Lepow-sky (Rutgers), & Dennis Shasha (Courant Institute).

The Canadian Mathematical Society was pleased to present lec-tures from their research prize winners, specifically, the CMS Jeffery-Williams Lecture, given by Ram Murty (Queen’s) and the CMS Krieger-Nelson Lecture, given by Leah Keshet (British Columbia).

A wide variety of fields of interest were represented in the sym-posia topics detailed belows:

Algebraic and Geometric Topology, George Peschke (Alberta), Laura Scull (British Columbia) & Peter Zvengrowski (Calgary).

Approximation Theory and Applied Harmonic Analysis, Bin Han & Rong-Qing Jia (Alberta).

Computational and Analytical Techniques in Modern Applications, Peter Minev (Alberta).

Conformal Field Theory, Terry Gannon (Alberta) & Mark Wal-ton (Lethbridge).

Design Theory and Coding Theory, John van Rees (Manitoba).

Discrete Mathematics, Vaclav Linek (Winnipeg).

Dynamical Systems, Michael A. Radin (Rochester Institute of Technology).

Industrial Mathematics, Biao Huang, Yanping Lin & Shijie Liu (Alberta).

Infinite Dimensional Dynamical Systems, Thomas Hillen (Alber-ta) & XiaoQiang Zhao (Memorial Univ. of Newfoundland).

Mathematical and Computational Finance, Tahir Choulli & Jie Xiong (Alberta).

New and Successful Courses and Programmes in Mathematics, Ted Lewis (Alberta).

Physics and Geometry, Maung Min-Oo (McMaster) & Eric Woolgar (Alberta)

Real Analysis, Erik Talvila (Alberta).

The Meeting Committee would like to acknowledge with much thanks the financial support of the following: The National Programme Committee (a joint funding body of the Centre de recherches mathématiques, The Fields Institute for Research in Mathematical Sciences, and The Pacific Institute for the Math-ematical Sciences), University of Alberta, Department of Math-ematical and Statistical Sciences,Conference Fund, Faculty of Science & Theoretical Physics Institute, Applied Mathematics Institute; University of British Columbia Faculty of Science & Mathematics Dept; University of Lethbridge; Perimeter Insti-tute for Theoretical Physics; Canadian Institute for Theoretical Astrophysics & Nelson, A Thomson Company.

CMS Winter Meeting 2003

December 6–8, 2003

Held at the Harbour Centre Campus

of Simon Fraser University

Org.: Meeting Director, Norman R. Reilly (SFU); Alastair Lachlan and

Malgorzata Dubiel (SFU).

Special sessions:Combinatorics, Petr Lisonek (SFU) & Brett Stevens (Carleton).

Dynamical Systems & Celestial Mechanics, Florin Diacu (UVIC).

Graphs and Matroids, Luis Goddyn (SFU) & Ladislav Stacho (SFU).

Harmonic Analysis, Izabella Laba (UBC) & Alex Iosevich (Mis-souri, Columbia).

History of Mathematics, J.Len Berggren (SFU).

Mathematical Biology, Leah Keshet (UBC).

Mathematical Education, Malgorzata Dubiel (SFU).

Model Theory and Recursion Theory, Robert Woodrow (Calgary) & Bradd Hart (McMaster).

Nonlinear Partial Differential Equations, Keith Promislow (SFU) & Rustum Choksi (SFU).

Number Theory, Michael Bennett (UBC), David Boyd (UBC), Peter Borwein (SFU), Imin Chen (SFU) & Stephen Choi (SFU).

Operator Algebras, Ian Putnam (UVIC) & Marcelo Laca (UVIC).

Quantum Cohomology and Mirror Symmetry, Kai Behrend (UBC).

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Representations of Associative Algebras, Vlastimil Dlab (Carleton) & Shiping Liu (Sherbrooke).

Universal Algebra and Lattice Theory, Jennifer Hyndman (UNBC).

Plenary Speakers:Tom Archibald (Acadia)France, Germany, and the making of modern mathematics

Deborah Ball & Hyman Bass (Michigan)The role of definitions in teaching and learning mathematics

Robert Calderbank (Princeton)Quantum computers and cellular phones

Andrew Granville (Montréal)Uncertainty principles in arithmetic

Anand Pillay (UIUC)Stable theories, examples, and applications

Madhu Sudan (Radcliffe Institute for Advanced Study)List decoding of error correcting codes

Coxeter-James LectureJingyi Chen (UBC)Recent developments in mean curvature flow of higher codimension

CMS Doctoral Prize LectureAlina Carmen Cojocaru (Princeton)Elliptic curves modulo p

Short-course on Cryptography:Neal Koblitz (Washington)Introduction to elliptic curve cryptography

Mike Mosca (Waterloo)Quantum computing and quantum cryptography

Doug Stinson (Waterloo)Introduction to cryptography

Hugh Williams (Calgary)Cryptography and number theory

The meeting was sponsored by the CMS, the National Program Committee (CRM, Fields, PIMS), Simon Fraser University, University of British Columbia, University of Calgary Depart-ment of Mathematics, University of Calgary Dean of Science,

University of Northern British Columbia.

Annual Meeting of the Statistical Society of Canada (SSC)

May 30 to June 2, 2004 , CRM, Université de Montréal

Organizers: Program Committee Chair, Christian Genest (Laval);

Local Arrangements Chair, Christian Léger (Montréal)

The thirty-second annual meeting of the Statistical Society of Canada was hosted by the Université de Montréal, and the Centre de recherches mathématiques. Over 550 registrants participated

in the meeting, which featured a wide range of sessions, including workshops of three SSC sections: Biostatistics, Survey Methods, and Business and Industrial Statistics.

The meeting was sponsored by the Centre de recherches mathé-matiques, the Fields Institute, PIMS, MITACS, Hydro Québec, the Université de Montréal, Pfizer, Laboratoires universitaires Bell University Laboratories, and Institut de la statistique du Québec.

The scientific program was extremely rich with 109 invited pa-pers and 142 contributed papers. Among the invited papers, the following addresses are especially noteworthy.

Presidential Invited Address:Kathryn Roeder (Carnegie Mellon)Discovering haplotype blocks in the human genome

Gold Medal Address:Mary Thompson (Waterloo)Understanding associations: implications for the design and analysis of longitudinal surveys

Special Invited Addresses of the Sections:Raymond Chambers (Southampton)Informative sampling and sampling information

Daryl Pregibon (Google, Inc.)Graph Mining

Richard Simon (US National Cancer Institute)Key features in the design and analysis of DNA microarray studies

Pierre Robillard Award Address (Best Thesis):Rachel MacKay Altman (Washington)Hidden Markov Models: Multiple Processes and Model Selection

Canadian Journal of Statistics Award Address:Belkacem Abdous (Laval), Kilani Ghoudi (United Arab Emirates), Bruno Rémillard (HEC Montréal) Nonparametric Weighted Symmetry Tests

24th Annual Meeting of CAIMS

July 16-20, 2003

Organizing Committee: Jacques Bélair (Montréal), (Président, Canada); Ilse

Ipsen (North Carolina State), (Président, E.-U.).

The Annual meeting of the Society was held in Montréal, June 16-20. For the first time, the meeting was formally joint with the Society for Industrial and Applied Mathematics (SIAM). There was close collaboration between the two Societies to jointly hold all activities (the scientific ones, foremost), in accord with the identity of each.

The number of participants, close to 550, was sizable for a CAIMS/SCMAI Annual meeting.(Of course, the geographi-

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cal origin of the majority of registrants (USA) suggests that the SIAM portion did attract a fraction of these). Two factors appar-ently negatively influenced this number: 1. a SARS effect, as par-ticipants from abroad cancelled in unusual numbers (SIAM had to postpone a meeting scheduled for Toronto the week of June 23 for this reason), and 2. the International Congress, ICIAM, in Sydney (Australia) in early July forced some people to make a geographical choice of destination.

The Organizing committee, in setting the scientific program, tried the usual balancing act of addressing the traditional areas of interest and strength of the Society members, and opening to ar-eas less developed inside the Society, where major developments are taking place, and in which mathematics is playing an increas-ing role. Anecdotal reports confirm that the overall flavour of the meeting was perceived as somewhat unusual. There were 10 plenary talks (including prize lectures), and 9 topical talks, which are semi-plenary lectures, i.e. only two talks in parallel. These were initiated at SIAM Annual meeting in 2002, and provide an interesting avenue between plenary and sessional talks. Also, there were ample parallel sessions, up to 8 simultaneous ones at one point: this is a consequence of the combined size of the meeting and desire of most attendees to present (an issue which is not significant at “traditional” CAIMS/SCMAI Annual meet-

ings). Overall, the meeting was successful, and of high quality.

AARMSThe Atlantic Association for Research in the Mathematical Sci-ences (AARMS) was founded in 1995. AARMS exists to encour-age and advance research in all mathematical sciences, including statistics and computer science, in the Atlantic region of Canada. In addition, AARMS acts as a regional voice in discussions of the mathematical sciences on a national level. Since its inception, AARMS has played an important role in the research activities in the Atlantic region, sponsoring or co-sponsoring numerous meetings and workshops. In the summer of 2002, AARMS initi-ated an annual Summer School for graduate students and prom-ising undergraduates.

Since June 2002, AARMS can count on stable long-term fund-ing thanks to co-sponsorship by the three mathematical institutes (CRM, Fields Institute, and PIMS) and the universities of New Brunswick, Memorial, and Dalhousie. Each of the six partners invests 30K$ per year into the Atlantic mathematical communi-ty. MITACS has also contributed important financial resources for industrial mathematical research in the Atlantic provinces. A Scientific Review Panel, including participation from the three institutes and the Atlantic mathematical community, helps the AARMS Director, Dr. Hermann Brunner, in the planning of scientific activities.

As part of the 2003-2004 thematic year on Geometric and Spec-tral Analysis, we are particularly proud to organize a joint work-shop with AARMS. The workshop is on singular integrals and analysis on CR manifolds. It was held in Halifax, Nova Scotia.

Here the list of the joint activities corresponding to the year2003-2004 of the CRM:

Workshop on Combinatorial Designs and Related TopicsJuly 14 - 18, 2003

Memorial University

Org.: Rolf Rees & Nabil Shalaby (Memorial)

15th Canadian Conference on Computational GeometryAugust 11 - 13, 2003

Dalhousie University

Org.: Michael McAllister (Dalhousie)

Second Annual AARMS Summer SchoolJuly 21 - August 15, 2003

Memorial University

Org.: Edgar Goodair (Memorial)

Courses were offered in:•Cryptography, by Hugh Williams (Calgary)•Financial Matters, by John van der Hoek (Adelaide)•Mathematical Biology, by Jianhong Wu (York)•Partial Differential Equations, by James Robinson (Warwick)

Workshop on Financial MathematicsAugust 17 - 20, 2003

Memorial University

Org.: Robert Elliott (Calgary), Edgar Goodaire

(Memorial), John van der Hoek (Adelaide)

APICS 2003 / AARMS Research Session in Linear AlgebraOctober 18 - 19, 2003

University of Prince Edward Island (UPEI)

Org.: Gordon MacDonald (UPEI), Heydar Radjavi (Dalhousie)

International Workshop on Wavelets – Theory and ApplicationsApril 26 - May 7, 2004

University of Prince Edward Island (UPEI)

Org.: Nasser Saad (UPEI)

AARMS-CRM Workshop on Singular Integrals and Analysis on CR ManifoldsMay 3 - 8, 2004

Dalhousie University

Org.: Galia Dafni (Concordia), Andrea Fraser (Dalhousie)

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CRM Prizes

January 2004: The director by interim of the Centre de recher-ches mathématiques (CRM) of l’Université de Montréal, Chris-tian Léger, and the Director of the Fields Institute for Research in Mathematical Sciences, Kenneth R. Davidson, are pleased to announce that the CRM-Fields Prize for 2004 is awarded to Professor Donald Dawson in recognition of his exceptional achievement and work in probability.

Donald Dawson, this year’s recipient, is one of the world’s lead-ing probabilists, having made seminal contributions to the study of spatially distributed stochastic processes and infinite-dimen-sional branching systems, among those being the Dawson-Wata-nabe superprocess. He received his B.Sc. from McGill in 1958 and his doctorate from MIT in 1963.

Professor Dawson taught at both McGill University and Car-leton University, where he is now Professor Emeritus. His lead-ership within the Canadian mathematical community includes a term as Director of the Fields Institute from 1996 to 2000. He is a Fellow of the Royal Society of Canada, as well as of the Inter-national Statistical Institute and the Institute of Mathematical Statistics.

Other honours include 1991 Gold Medal Lecture of the Statisti-cal Society of Canada, the 1994 Jeffery-Williams lecture of the CMS, an invited lecture at the 1994 ICM, as well as the Fields Institute’s Distinguished Lecture Series in the Statistical Sci-ences. His numerous editorial contributions include serving as co-editor-in-chief of the Canadian Journal of Mathematics. He has served his profession through numerous NSERC and CMS committees, and is currently President-Elect of the Bernoulli So-ciety for Mathematical Statistics and Probability.

CRM-Fields Institute Prize was awarded to Donald Dawson

In 1994, the Centre de recherches mathématiques (CRM) and the Fields Institute announced the creation of a new prize to be awarded for exceptional contributions to the mathematical sciences. The recipient of the prize is chosen by the Advisory Committee of the CRM and the Scientific Advisory Committee of the Fields Institute according to the criterion of excellence in research. The prize consists of both a $5,000 award and a medal, and the winner is required to give a lecture at the CRM and the Fields Institute. The past recipients are: H.S.M. Coxeter (1995), G.A. Elliot (1996), J. Arthur (1997), R.V. Moody (1998), Stephen A. Cook (1999), Israel Michael Sigal (2000), William T. Tutte (2001), John B. Friedlander (2002), John McKay and Edwin Perkins (2003).

Professor Donald Dawson during his presentation to the CRM, Friday November 12, 2004.

Professor Donald Dawson receives the CRM-Fields Prize from CRM director, Professor François Lalonde

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The André-Aisenstadt Prize was awarded to Vinayak Vatsal of the University of British Columbia. Dr. Vatsal obtained his Ph. D. from Princeton University in 1997 under the supervision of A. Wiles. After spending two years as a post-doctoral fellow at the University of Toronto, he joined the staff at the University of British Columbia in 1999. He works in Arithmetic Algebraic Geometry, more precisely in the study of L-functions of elliptic curves. His most spectacular work to date was on the uniform distribution of Heegner points, in which he introduced in a novel and unexpected fashion ideas from ergodic theory. He was thus able to prove a fundamental conjecture of Mazur concern-ing the L-functions of elliptic curves over anticyclotomic towers (now the Vatsal-Cornut theorem).The Prize was awarded to Dr. Vatsal at a ceremony to held April 2, 2004 at CRM.

André-Aisenstadt Prize 2003-2004 was awarded to Vinayak Vatsal

Created in 1991, the André-Aisenstadt Mathematics Prize is intended to recognize and reward talented young Canadian mathematicians. The Prize, which is given for research achievement in pure and applied mathematics, consists of a $3000 award. The recipient is chosen by the CRM Advisory Committee. At the time of nomination, candidates must be Canadian citizens or permanent residents of Canada, and no more than seven years from their Ph.D. The previous winners of the André-Aisenstadt Prize were: Niky Kamran (1991), Ian Putnam (1992), Michael Ward and Nigel Higson (1994), Adrian S. Lewis (1995), Henri Darmon and Lisa Jeffrey (1996), Boris Khesin (1997), John Toth (1998), Changgeng Gui (1999), Eckhard Meinrenken (2000), Jingyi Chen (2001) and Alexander Brudnyi (2002).

Courtesy UBC Science, ©2002 Hot Digital Studios.

Vinayak Vatsal

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Coming from elementary particle physics, Jiri Patera was at-tracted very early to the underlying mathematics, and in 1965, while a postdoctoral fellow at the Université de Montréal, he fo-cused his attention on the theory of Lie groups and Lie algebras. The numerous contributions he made with various collabora-tors (amongst others, P. Winternitz, H Zassenhaus, R. Sharp and R. Moody) have left an indelible mark on this discipline, in which he is now considered to be one of the best special-ists in the world. The areas where his contributions were crucial include the representation theory of compact and non-compact Lie groups, generating functions in group representation theory, discrete Fourier analysis on simple and semi-simple Lie groups, and Lie algebra gradings. In 1992, in collaboration with R. Moody, he undertook a remarkable series of investigations on the mathematical properties of quasi-crystals.

CAP-CRM Prize 2004 was awarded to Jiri Patera

Awarded for the first time in 1995, the CAP-CRM Prize is given for outstanding contributions to theoretical and mathemati-cal physics by the Canadian Association of Physicists and CRM. It consists in a $2000 award and a medal. Previous winners were Werner Israel (1995), William G. Unruh (1996), Ian Affleck (1997), J. Richard Bond (1998), David J. Rowe (1999), Gordon W. Semenoff (2000), André-Marie Tremblay (2001), Pavel Winternitz (2002), and Matt Choptuik (2003).

Combining a deep physical intuition with an exceptional knowl-edge of mathematics, Jiri Patera has displayed much inventive-ness in proposing new approaches to old problems. He has always managed to choose research topics likely to have prac-tical applications, as testified by the six books he co-authored, which give tables on weight multiplicities and branching rules. His work has had an impact on nuclear and elementary particle physics, quantum chemistry and solid state physics. His research on quasi-crystals even had implications in cryptography.

After staying in Soviet Union for many years, mainly in Mos-cow and Dubna, Jiri Patera obtained his Ph.D. in 1964 from the Charles University in Prague. He joined the CRM in 1969, and has been a member of the Department of mathematics and statistics of the Université de Montréal since 1983.

CAP-CRM Prize 2004 was awarded to Jiri Patera of Université de Montréal.

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CRM-SSC Prize was awarded to Randy Sitter

In 1999, the Centre de recherches mathématiques (CRM) and the Statistical Society of Canada created the CRM-SSC Prize in statistics in recognition of outstanding contributions to the Statistical Sciences during the recipient’s first 15 years after earning a doctorate. The CRM-SSC Prize in Statistics consists of a $3000 award and a medal. The recipient is chosen by a joint CRM/SSC advisory committee, consisting of three members named by the SSC and two, including a president, by the CRM. Previous winners were Christian Genest (1999), Robert Tibshirani (2000), Colleen Cutler (2001), Larry A. Wasser-man (2002) and Charmaine B. Dean (2003).

The CRM-SSC Prize in Statistics was awarded to Dr. Randy R. Sitter, Professor, Department of Statistics and Actuarial Science, Simon Fraser University (SFU), for his outstanding contributions to the statistical sciences, par-ticularly in survey sampling and industrial statistics. The announcement was made at the 32nd Annual Meeting of the Statistical Society of Canada (SSC), held in Montréal, Québec, May 30 to June 2, 2004. This pres-tigious award, jointly sponsored by the SSC and the Centre de recherches mathématiques de Montréal (CRM), is given each year to a Canadian statistician in recognition of outs-tanding contributions to the discipline during the recipient’s first 15 years after earning a doctorate.

Randy Sitter was born in 1961 in New West-minster, British Columbia. When he was 9, his family moved to Prince George where he attended high school with Deanna, now his wife. He completed a Bachelor’s degree in Mathematics in 1984 and a Master’s degree in Statistics in 1986 at the University of British Columbia (UBC). He switched to Statistics after a Mathematics Professor once told him “You’re good.... but you’re not that good. Perhaps you should go into statistics.” To finance his studies at UBC, Randy Sitter supported himself doing carpentry and tree planting. Based on data records he kept of his career as a reforester (as might be expected of a future statistician), he estimates that he planted over 300,000 seedlings, which amounts to some 300 hectares of forest regenerated for the benefit of the province.

To pursue doctoral studies, Randy Sitter went to the University of Wisconsin in Madison and worked under the supervision of Professor C.F. Jeff Wu. When the latter accepted a position at the University of Waterloo, Randy Sitter followed him. In 1990, he defended there his Ph.D. thesis entitled “Resampling procedures for complex survey data.” As early as January 1990, he became As-sistant Professor in the Department of Mathematics and Statistics at Carleton University. While there, he played a major role in the

development of the department’s computing resources. He moved to the Department of Mathematics and Statistics at SFU in January 1995 and then became a charter member of the new Department of Statistics and Actua-rial Science in May 2001.

Randy Sitter’s thesis concerned bootstrap methods which are applicable to complex survey designs of the sort actually in use at statistical agencies. Over the years, he has worked in a variety of areas, making major contributions in survey sampling and in experimental design and industrial statistics. Within these areas, he has worked on variance estimation in complex surveys, imputation, empirical likelihood methods in surveys, opti-mal design for bioassays, the use of orthogonal multi-arrays for balanced repeated sampling, minimum aberration designs, and more. He published extensively in the most influential journals such as Technometrics, Biometrika, the Journal of the American Statistical Asso-ciationand The Canadian Journal of Statistics, among many others.

Since he earned his doctorate, Randy Sitter has also made outs-tanding contributions to the profession, notably through graduate supervision, editorial service, involvement in professional statisti-cal societies, the organization of meetings and active participation in the growth of his department at SFU. He has been an Associate Editor of Survey Methodology, Biometrics, Technometrics, and The Canadian Journal of Statistics. Since January 2004 he is Editor-Elect of Technometrics. He is currently supervising four doctoral students; two more have already graduated: Changbao Wu, now at the University of Waterloo, and Derek Bingham, now holding a Tier II Canada Research Chair at SFU. At the Master’s level, Randy has had nine students graduate and is cur-rently supervising two more. A former member of the Executive Committee of the Statistical Society of Ottawa and of the Board of Directors of the SSC, he has also been President of the Survey Methods section of the SSC.

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In addition to having contributed in a major way to the develop-ment of the Department of Statistics and Actuarial Science at SFU, Randy Sitter is a crucial component in its basketball program. He began playing ball at Kelly Road Secondary School. After his first year at UBC, he returned to Prince George to play for the College of New Caledonia basketball team. They were provincial champions in the season 1980-81 and third at the Canadian championships that year. Because “he is tall, but not that tall,” Randy Sitter eventually returned to UBC to complete his degree, a choice for which his colleagues at SFU are thankful.

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CRM-ISM Colloquium Series

The CRM, together with the Institut des sciences mathématiques (the Québec university graduate mathematics consortium), runs two Montréal colloquium series, one in mathematics and another in statistics (the latter jointly with GERAD). These series offer during the academic year survey talks by distinguished mathematicians and statisticians on topics of current interest.

CRM-ISM Mathematics Colloquium Responsibles: Iosif Polterovich (Université de Montréal)

2004

April 30, 2004Jill Pipher (Brown)Multiparameter Fourier Analysis

April 23, 2004Terry Lyons (Oxford)Rough Paths

April 16, 2004Gordan Savin (Utah)Exceptional groups and the arithmetic of cubic fields

March 26, 2004Alina Stancu (Montréal)Curvature flows from the viewpoint of convex geometry

March 19, 2004Charles Newman (Courant Institute of Mathematical Sciences)Continuum Nonsimple Loops and 2D Critical Percolation

March 12, 2004Yakov Sinai (Princeton)Mathematical Hydrodynamics

March 5, 2004Rafe Mazzeo (Stanford)Positive scalar curvature and Poincare-Einstein fillings

February 27, 2004Ernst Hairer (Genève)Are linear multistep methods suitable for long-time integration ?

February 20, 2004Dorothy Buck (Brown. & IHES)The Topology of DNA-Protein Interactions

February 13, 2004François Bergeron (UQAM)Invariants de groupes finis et leurs applications à la combinatoire

January 30, 2004Ravi Vakil (Stanford)A geometric Littlewood-Richardson rule

January 23, 2004Eckhard Meinrenken (Toronto)Chern-Weil theory and Lie algebras

January 16, 2004Victor Ivrii (Toronto)Sharp Spectral Asymptotics for Operators with Irregular Coef-ficients

2003

December 5, 2003Victor Havin (St. Petersburg & McGill )On the separation of singularities of analytic functions

November 28, 2003Octav Cornea (Montréal)The Morse complex

November 21, 2003Stephane Fischler (École Normale Supérieure & Ottawa)Irrationality of zeta values (after Apéry, Rivoal, ...)

October 24, 2003Mikhail Sodin (Tel-Aviv)Growth, zeroes, and area estimates. Variations on the theme

October 17, 2003 Jonathan Pila (McGill)Integer and rational points on curves and surfaces

October 10, 2003Robert Russell (Simon Fraser & McGill )Numerical solution of PDEs using moving grids -- an overview

September 26, 2003Igor Pak (MIT)The nature of partition bijections

September 19, 2003Felix Finster (Regensburg)The Dirac Sea and the Principle of the Fermionic Projector

September 12, 2003Gianni Cassinelli (Genoa)Group Theoretical Quantum Tomography

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CRM-ISM-GERAD Statistics Colloquium

Responsibles: Pierre Duchesne (Montréal), Brenda MacGibbon (UQAM), Aruch Sen (Concordia), & George Ph. Styan (McGill).

2004

April 23, 2004Christian Genest (Laval)Tests d’indépendance fondés sur le processus de copule empirique

April 16, 2004David Dickson (Melbourne)The distribution of the time to ruin

April 2, 2004Winfried Stute (Giessen, Germany)Nonparametric Model Checks in Statistics

March 26, 2004Jean-Pierre Dion (UQAM)Quasilikelihood Methods in Size-Dependent Branching Processes with Application to Polymerase Chain Reactions (PCR)

March 19, 2004David Binder & Georgia Roberts (Direction de la méthodologie, Statistique Canada)Analysis Issues for Data from Complex Survey

March 12, 2004Susan A. Murphy (Michigan)Dynamic Treatment Regimes, Multistage Decisions and Reinforce-ment Learning

March 5, 2004Jonnagaddan N.K. Rao (Toronto)Practical Issues in Model-Based Small Area Estimation

2003

November 28, 2003Gabor J. Szekely (Bowling Green State Univ. & Hungarian Academy of Sciences, Budapest)Absolute Statistics: E and s

November 21, 2003Bimal Sinha (UMBC)On some aspects of Tukey’s test for nonadditivity with one d.f.

October 31, 2003A.S. Hedayat (Univ. of Illinois, at Chicago)Optimal and efficient crossover designs

October 17, 2003John Petkau (UBC)Neutralizing Antibodies and the Efficacy of Interferon Beta-1b in Multiple Sclerosis Clinical Trials

October 10, 2003Bruno Remillard (HEC)Weighted-symmetry and applications

September 26, 2003Jim Berger (Duke)Statistical Validation of Computer Models

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CRM PartnersWithin its general mandate of promoting mathematical research, the CRM maintains a wide network of collaborations at the local, national, and international levels.

A National Institute of International Stature

The CRM is strongly committed to its national mission and takes measures to ensure that the largest possible number of scientists across Canada benefits from its activities and become involved in their planning. For instance, it appoints to its Advisory Committee eminent Canadian scientists from various parts of the country; it is present at all important forums where the future directions of the Canadian mathematical sciences are discussed; it urges its organiz-ers to make efforts to ensure the participation of the Canadian spe-cialists in their activities; it organizes and supports scientific events across the country; it collaborates with Canadian institutes, socie-ties and associations. A specific budget is set aside each year for the participation of Canadian graduate students in its programs. The CRM is the only national institute that operates in the two official languages of Canada and it is highly visible on the international scene. In keeping with its national role, it coordinates its activi-ties with the Fields Institute, PIMS, the Canadian Mathematical Society (CMS), the Canadian Applied and Industrial Mathematics Society (CAIMS), the Statistical Society of Canada (SSC), the Ca-nadian Association of Physicists (CAP), and other societies as well as with other institutes abroad.

The Fields Institute (FI) and the Pacific Institute for the Mathematical Sciences (PIMS)

Since the early 1990’s two other research institutes have joined the CRM on the Canadian scene: Toronto’s Fields Institute (FI), and the Pacific Institute for Mathematical Sciences (PIMS). As well as coordinating their scientific activities, the three institutes have worked closely on a variety of initiatives, the most important of which has been the Mathematics of Information Technology and Complex Systems, (see Industrial Collaborations section).

There are several other initiatives worthy of mention. One of these is the National Program Committee, described in a separate sec-tion. We also participate to the development of the mathematical sciences in the Atlantic provinces though AARMS; see the section on AARMS. The National Program on Complex Data Structures, funded through NSERC’s last reallocation exercise, is a joint initia-tive of the three institutes and the Canadian statistical community. The broad goal of the program is to foster nationally coordinated projects with substantial interactions with the large community of scientists involved in analysis of complex data sets, and to establish a framework for national networking of research activities in the statistical community.

Other initiatives involved two institutes, such as the CRM-Fields prize awarded in recognition of outstanding accomplishments in the mathematical sciences in Canada. It was created in 1994. This year’s winners are John McKay of Concordia University and Edwin Perkins of the University of British Columbia. The administra-

tive responsibility in this matter alternates each year between the CRM and the FI. Scientific collaboration continues between FI and CRM, with a close coordination of the activities for the theme years 2003–2004 in analysis and partial differential equations with two series of two workshops that alternated between the two in-stitutes.

Associations and Professional Societies

The CRM maintains close ties with the different professional soci-eties in the mathematical sciences: CMS, CAIMS, SSC, and CAP. The president of the CMS is an ex-officio member of the CRM ad-visory committee. We also financially support a number of initia-tives of the CMS, such as the mathematical camps, the Canadian School Mathematics Forum 2003, as well as the travel grant pro-gram for students who will attend the joint Canada-France meet-ing in Toulouse in 2004. Together with the other institutes, the CRM organizes or sponsors special sessions at the CMS, CAIMS, and SSC meetings. The CRM awards a prize each year jointly with the SSC; similarly, together with CAP, it awards a prize each year in mathematical and theoretical physics. There is a section on this year’s prize winners elsewhere in this report. Moreover, the CRM hosted host the 2004 Annual Meeting of the SSC.

International Collaboration

In 2003-2004, on the international scene, the CRM collaborated or received financial assistance from the National Science Foun-dation (NSF), the Banff International Research Station (BIRS), INSERM in Paris, the Institute of Electrical and Electronics En-gineers (IEEE), Alcatel, and the Institute for Mathematics and its Application (IMA).

In its publications, the CRM is continuing its partnership with the American Mathematical Society, in particular with its two series of joint publications, the CRM Monograph Series and the CRM Proceedings and Lecture Notes. It also has series with Springer-Verlag, in statistics and in mathematical physics. This year, CRM has also published a book jointly with the Institute of Mathemati-cal Statistics. The CRM has exchange agreements with Fields In-stitute, PIMS, MSRI (Mathematical Sciences Research Institute), the Institute for Mathematics and its Applications, École Normale Supérieure (France), the Isaac Newton Institute, the Institut des Hautes Études Scientifiques (IHES, France), and the Banff Inter-national Research Station.

Our Academic Partners

All this activity rests on a solid base of cooperation with universities in the region, in particular the Montréal universities, and most par-ticularly the Université de Montréal, whose support for the CRM has been indefatigable. The Université de Montréal releases five of

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its faculty members to work at the CRM each year, and the sup-port of these faculty members is an essential asset for the CRM’s scientific activities. There is in addition a regular program of teaching release with the other Montréal universities, bringing the equivalent of another two positions to the CRM each year. On an ad-hoc basis linked to the theme program, the CRM has also been arranging release of research personnel from nearby universities such as Laval, Sherbrooke, Queen’s and Ottawa. The partnerships of the CRM with the other research institutes in the Montréal area have been very profitable. The collaborations are mentioned in the section on industrial collaborations.

This year, the CRM initiated a new large-scale partnership with Québec universities that has permitted the establishment of eight interuniversity laboratories headed by the CRM. With the financial support of the Université de Montréal, McGill University, Univer-sité de Québec à Montréal, Concordia University, and Université Laval as well as grants from Fonds de recherche québécois sur la nature et les technologies (FQRNT) of Québec and of NSERC, CRM finances the activities of the eight laboratories representing the most active branches of the mathematical sciences. These labo-ratories are the scene of scientific vitality par excellence and serve to feed the national and international scientific programs of the CRM. Please refer to the section on the Research laboratories for reports describing the activities of each laboratory.

CRM is also pleased to announce a new initiative with the University of Ottawa that began in 2003-2004. In partnership with the Uni-versity of Ottawa, the CRM co-finances postdoctoral fellowships, a series of CRM-University of Ottawa conferences and teaching releases so that University of Ottawa faculty members can undertake research collaborations with colleagues in the CRM’s laboratories or to participate in CRM scientific activities..

Neuro-imaging initiative in Québec

In recent years, CRM’s PhysNum laboratory has developed a strong collaborative network with various partners in neuro-imaging in the Montréal area. This network was formalized with the constitution of the “Regroupement Neuro-imagerie Québec” (RNQ) under the umbrella of the Institut Universitaire de Gériatrie in Montréal. RNQ, with its 70 researchers, has recently purchased some key equipment in neuro-imaging through a very large grant ($11M). One of the strongest alliances of CRM within that network is its association with the INSERM laboratory for brain-imaging at Jus-sieu - La Salpêtrière, France (director: Habib Benali).

Institut des sciences mathématiques

Another important vehicle for collaboration with the Québec uni-versities is the Institut des sciences mathématiques (ISM). This in-stitute, which encompasses most of Québec’s universities, is prin-cipally concerned with coordinating graduate training. The links with research are obvious, and indeed, the CRM and the ISM have a long-standing partnership, in particular in offering postdoctoral fellowships, in organizing two series of CRM-ISM colloquium, one in mathematics and one in statistics, and in organizing special courses for the CRM’s thematic programs. Since Summer 2003, the CRM participate in the undergraduate summer scholarships program, which allows postdoctoral fellows to supervise under-graduate students

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Industrial Collaborations

MITACS

This network of centres of excellence on Mathematics of Informa-tion Technology And Complex Systems (MITACS) is one of 21 such networks set up by the federal government. MITACS was put together by the three Canadian mathematical institutes (CRM, Fields, PIMS) in 1998, and research began in the spring of 1999.

Network for computing and mathematical Modelling (ncm2)

The CRM serves as the organizational centre for the Network for Computing and Mathematical Modelling, ncm

2, a collaboration

which allows the network to respond to the needs of industry in a large number of fields related to a common area of computing and mathematical modelling, mostly around five major themes: (1) risk management, (2) information processing, imaging and parallel computing, (3) transport and telecommunications, (4) health and (5) electronic commerce.

The five centres that established the network were the CRM, the Centre de recherche en calcul appliqué (CERCA), the Center for In-teruniversity Research and Analysis on Organizations (CIRANO), the Center for Research on Transportation (CRT), and the Group for Research in Decision Analysis (GERAD). Since then, three new members joined the network: the Cooperative Centre for Re-search in Mesometeorology (CCRM), the Centre de Recherche Informatique de Montréal (CRIM) and the Institut National de la Recherche Scientifique – Télécommunications.

The network organized the following activities:

ncm2Grande Conférence presents

Douglas N. Arnold, (Director of the Institute for Math-ematics and its Applications)

From Exact Sequences to Colliding Black Holes: Differential Complexes in Numerical Analysis

October 16, 2003Workshop on Cerebral Plasticity: Imaging and Modeling

Organized by CRM

October 30-31, 2003

Workshop on Environment: Risk and ModelingOrganized by GERAD with CRM and CIRANO

May 6-7, 2004

Bell University Laboratories

The CRM is an active participant in the ncm2’s Bell University

Laboratories, part of a joint project between the ncm2 and Bell.

The laboratories aim at creating innovations in the field of mul-timedia research and applications (mainly interactive applications aimed at the general public, electronic commerce applications and new generations of evolved networks) as well as at promoting the training of a highly qualified, international calibre workforce in these areas.

The main vehicles for the CRM’s efforts in this area are the research networks to which it belongs. There are two of these, one the Network for Computing and Mathematical Modelling (ncm

2), involving eight research centres in the Montréal area and MITACS,

a national network focussing on the mathematics of information technology and complex systems.

CICMA

Research Laboratories

The CRM now encompasses eight research laboratories at the heart of the Québec mathematical community. These research centers act as focal points for local scientifi c activity and participate actively in the science direction of the CRM.

DirecteurHenri Darmon (McGill)Algebraic number theory, geometry, arithmetic, L-functions, diophantine equations, elliptic curves.

Chris J. Cummins (Concordia)Group theory, modular functions, Moonshine.

Chantal David (Concordia)Analytical number theory, L-functions.

Jean-Marie De Koninck (Laval)Analytic number theory: distribution of prime numbers, factorisation of num-bers, asymptotic behaviour of arithmetic functions, Riemann zeta function.

Dave Dummit (Vermont)Théorie algébrique des nombres, géomé-trie algébrique arithmétique, mathémati-ques computationnelles.

David Ford (Concordia) Algorithmic number theory.

Eyal Goren (McGill)Arithmetic geometry, algebraic number theory, moduli spaces of Abelian verieties, Hilbert modular forms, p-adic modular forms.

Andrew Granville (Montréal)Analytic number theory, arithmetic geometry, combinatorics.

Adrian Iovita (Concordia)Number theory, p-adic cohomology.

This centre comprises researchers working in number theory, group theory and algebraic geometry. Contemporary number theory follows two major courses. On the one hand, there is the theory of special values of L-functions attached to arithmetic objects, originating in the work of Gauss and Dirichlet and lead-ing to the modern conjectures of Deligne, Beilinson and Bloch-Kato. On the other hand, the Langlands program postulates a close link between arithmetic L-functions and automorphic representations. An area where these two currents intersect is the study of elliptic curves. The center is particularly well represent-ed in this regard with Darmon, Iovita, and Kisilevsky. CICMA also acquired a new expertise in many aspects of analytic number theory with the recent arrival of Andrew Granville, one of the leaders in the fi eld. On the group theory side, Kharlampovich

and Miasnikov are world-renowned specialists on group variet-ies and McKay is one of the originators of the moonshine pro-gram.

Among the problems to be studied by the group in the com-ing years include the construction of rational points on elliptic curves both from algorithmic and theoretical viewpoints; Zeta functions of varieties over fi nite fi elds on the algorithmic ap-proach; canonical lifting of elliptic curves and Abelian varieties; cryptography, Abelian varieties, and many aspects of analytic number theory, as averages of special values of L-functions, dis-tribution of prime numbers and prime divisors, and problems of additive number theory.

Members of laboratory CICMA Members of laboratory CICMA

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The traditional Québec-Vermont Number Theory Seminar was held every two weeks in 2003-2004, with speakers from eve-rywhere in the world were came to lecture on the latest programs in the fi elds: More details can be found at http://cicma.mathstat.concordia.ca/faculty/chantal/QVNTS/schedule0304.html.

Speakers: Scott Ahlgren (Urbana), Gil Alon (CICMA), Fabrizio Andreatta (Univ. of Padova), Michael Bennett (UBC), Valentin Blomer (Univ. of Toronto & Stuttgart Univ.), Mei-Chu Chang (UC Riverside), Peter Clark (CICMA), Keith Conrad (Con-necticut), John Conway (von Neumann Professor, Princeton University), Henri Darmon (McGill), Stéphane Fischler (Ecole Normale Supérieure), Alexandru Ghitza (CICMA), Eyal Goren (McGill), Ben Green (Cambridge), Christopher Hughes (Ameri-can Institute of Mathematics), Adrian Iovita (Concordia Univ.), Habiba Kadiri (CICMA), Payman Kassaei (CICMA), Kiran Kedlaya (MIT), Chandrashekhar Khare (Utah), Sandor Kovacs (Washington), Alan Lauder (Oxford), Greg Martin (UBC), Jean-Francois Mestre (Université Paris 7), Elena Montavan (Berkeley), Robert Osburn (Queens), Ambrus Pal (CICMA), Jonathan Pila (McGill Univ.), Carl Pomerance (Dartmouth College), Fernando Rodrigues Villegas (Texas), Jonathan Sands (Univ. of Vermont), Gordan Savin (Utah), David Savitt (CICMA), Norbert Schlo-miuck (Univ. de Montréal), Peter Schneider (Muenster Univ. / Univ. of Chicago), Igor Shparlinski (Macquarie Univ.), Jack Sonn (Technion), Kannan Soundararajan (Univ. of Michigan), Harold Stark (UCSD), Cam Stewart (Waterloo), Lucien Szpiro (CUNY), Eric Urban (Columbia), Nike Vatsal (UBC), Gary Walsh (University of Ottawa), June Zhu (McMaster).

A seminar on cohomology was organized by Eyal Goren. Notes from this seminar are currently written by Eyal Goren and several of the CICMA postdoctoral fellows, and the fi nal result will be a book on the subject. More details can be found at http://www.math.mcgill.ca/goren/SeminarOnCohomology.html.

Speakers: Gil Alon, Andrew Archibald, Gabriel Chenevert, Pete Clark, Alex Ghitza, Eyal Goren, Matthew Greenberg, Payman Kassaei, Ratnadha Kolhatkar, Elena Mantovan, Marc-Hubert Nicole, David Savitt, Shahab Shahabi.

A seminar organized by Henri Darmon and Adrian Iovita on automorphic forms, quaternion algebras and the L-invariant of Greenberg and Stevens was held during the winter term. This lead to the joint paper “Families of automorphic forms on defi nite quaternion algebras and the Mazur-Tate-Teitelbaum conjectures in higher weight” by Darmon and Iovita, which is currently in preparation.

An informal workshop, with participants Chantal David, Jack Fearnley, Hershy Kisilevsky, and occasionnally Andrew Gran-ville, was formed to discuss questions on analytic rank of twisted L-functions of elliptic curves and random matrix theory. This leads to 2 joint plublications of David, Fearnley and Kisilevsky on links between vanishing of L-functions and random matrix theory.

S e m i n a r s 2 0 0 3 - 2 0 0 4 - L a b o r a t o r y C I C M A S e m i n a r s 2 0 0 3 - 2 0 0 4 - L a b o r a t o r y C I C M A

Olga Kharlampovich (McGill)Combinatorial theory of groups and Lie algebras.

Hershy Kisilevsky (Concordia)L-functions, Iwasawa theory, elliptic curves, class fi eld theory.

Claude Lévesque (Laval)Algebraic number theory, units, class number, cyclotomic fi elds.

Michael Makkai (McGill)Mathematical logic.

John McKay (Concordia)Computational group theory, sporadic groups, computation of Galois groups.

Alexei Miasnikov (McGill)Group theory.

Ram Murty (Queen’s)Number Theory: Artin’s conjecture, Elliptic curves, Modular Forms, Auto-morphic forms, Langlands Program, Selberg’s conjectures, Sieve Methods, Cryptography.

Jonathan Pila (McGill)Number theory, especially algorithmic and diophantine problems.

Damien Roy (Ottawa)Transcendental Number Theory.

Peter Russell (McGill)Algebraic geometry.

Francisco Thaine (Concordia)Cyclotomic fi elds, cyclotomy, rational points on curves.

Members of CICMA laboratory - continued

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CIRGET

Geometry and topology are fundamental disciplines of mathe-matics whose richness and vitality have been evident throughout human history and refl ect their deep link to our experience of the universe. They are at a crucial crossing point of modern mathematics and in effect several domains of mathematics have recently shown a strong trend towards a geometrization of ideas and methods: two cases in point are mathematical physics and number theory.

During the last twenty-fi ve years, a group of researchers of international calibre in geometry and topology has been hired by Quebec universities. The research centre, based at UQAM, now comprises fi fteen professors-researchers together with a large number of postdoctoral fellows and graduate students. The main themes to be pursued in the coming years include Dehn surgery and Thurston geometrization; quantization of Hitchin systems and geometric Langlands program; classifi cation of special Kähler metrics; the study of symplectic invariants, especially in dimen-sion 4; Hamiltonian dynamical systems.

DirecteurSteven Boyer (UQAM)Low-dimensional geometry and topol-ogy.

Syed Twareque Ali (Concordia)Coherent states, wavelets, quantization techniques, harmonic analysis

Vestislav Apostolov (UQAM)Complex geometry, Kähler geometry, special metrics.

Abraham Broer (Montréal)Algebraic geometry, Lie theory, represen-tation theory, invariant theory.

Olivier Collin (UQAM)Low-dimensional topology, differential geometry, gauge theory.

Octavian Cornea (Montréal)Algebraic topology, dynamical systems.

John Harnad (Concordia)Geometric methods in mathematical physics, integrable systems.

Jacques Hurtubise (McGill)Algebraic geometry, integrable systems, gauge theory, moduli spaces.

André Joyal (UQAM)Algebraic topology, category theory.

Niky Kamran (McGill)Differential geometry, partial differential equations.

François Lalonde (Montréal)Symplectic topology and geometry, global analysis, infi nite dimensional transformation groups.

Iosif Polterovich (Montréal)Complex analysis, functional analysis, spectral theory, potential theory.

Peter Russell (McGill)Algebraic geometry.

John Toth (McGill)Spectral theory, semi-classical analy-sis, micro-local analysis, Hamiltonian mechanics.

Daniel Wise (McGill)Geometric group theory, low-dimensio-nal topology.

M e m b e r s o f t h e l a b o r a t o r y C I R G E T M e m b e r s o f t h e l a b o r a t o r y C I R G E T

CIRGET

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In 2003-04, CIRGET updated and consolidated its infrastructure: the website was redesigned (http://www.cirget.uqam.ca), a da-tabase was created, and the CIRGET computer lab at UQAM was remodeled and its equipment brought up-to-date with funding, in part, from one of our FQRNT team grants. The goal to make the lab as fl exible as possible was achieved: users can now work from a variety of platforms including Macintosh, Windows, Linux, and Unix. We are in the process of installing a wireless network in the lab.

CIRGET’s scientifi c activity continued to fl ourish. Six of its members obtained a four-year grant from the NSERC Leadership Sup-port Initiative (LSI) programme in September 2003, one of just seven such grants awarded across the country. We intend to use the funding to organize eight thematic semesters.

Two working groups were set up during the year. One, on J-holomorphic curves and their applications, was organized by François Lalonde and met weekly at the Université de Montréal. The other, on geometrization and Ricci fl ow, was organized by Vestislav Apostolov, and met at UQAM.

Two CIRGET workshops were held. John Harnad and Jacques Hurtubise organized a workshop on tau-functions which took place at the CRM March 19-20. The speakers and their titles were: • Marco Bertola (Concordia), Isomonodromy tau functions and matrix models• John Harnad ( Concordia), Character expansion of tau functions• Dmitri Korotkin (Concordia), Isomonodromic tau-function and G-function of Hurwitz Frobenius manifolds• Vladimir Matveev (Université de Bourgogne et Steklov - St. Petersburg), Discrete versions of Darboux-Paschl-Teller potentials• Alexey Kokotov (Concordia), Tau-functions on spaces of holomorphic differentials and determinants of Laplace operator with conical

singularities on Riemann surfaces • Yousuke Ohyama (Osaka), A new class of Painlevé transcendents; monodromy solvable solutions• Andrei Kapaev (Research Center of Innovation and Developments - St. Petersburg), Large N asymptotics of spectral curves• Jacques Hurtubise (McGill), The geometry of Calogero-Moser systems

The second workshop, Trends in 3-manifolds, was organized by two CIRGET postdoctoral fellows, Benjamin Klaff and Stephan Tillmann. It took place May 1-2 at UQAM. The speakers and their titles were:• Ian Agol (University of Illinois at Chicago), Tameness of hyperbolic 3-manifolds• Danny Calegari (California Institute of Technology), Quasigeodesic fl ows and universal circles• Nathan Dunfi eld (California Institute of Technology), Does a random 3-manifolds fi ber over the circle?• Stavros Garoufalidis (Georgia Institute of Technology), The geometry of the Jones polynomial• Marc Lackenby (Oxford), A characterization of large, fi nitely generated groups• Saul Schleimer (University of Illinois at Chicago), Heegaard splittings and Haken’s problem• Genevieve Walsh (Austin), Virtually Haken fi llings of fi bered knot complements

CIRGET members have also been active in organizing events at the CRM, BIRS, PIMS as well as elsewhere in the world.

Highlights of the activities of the laboratory and of its members 2003-2004 Highlights of the activities of the laboratory and of its members 2003-2004 Highlights of the activities of the laboratory and of its members 2003-2004

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S e m i n a r s 2 0 0 3 - 2 0 0 4 – L a b o r a t o r y C I R G E TS e m i n a r s 2 0 0 3 - 2 0 0 4 – L a b o r a t o r y C I R G E T

In 2003-04, the Geometry-Topology Seminar, organized by Olivier Collin, had 32 speakers of whom 26 were from outside Mon-treal. The Geometric Group Theory Seminar, organized by Dani Wise, met 19 times and the CIRGET Junior Seminar, organized by Baptiste Chantraine, met 26 times.

Geometry-Topology Seminar

Responsible: Olivier CollinSpeakers: Tara Brendle (Cornell), Denis-Charles Cisinski (Paris 7), Olivier Collin (UQAM), Daryl Cooper (Univ. of California at Santa Barbara), Zindine Djadli (Cergy-Pontoise), Tolga Etgu (McMaster), Stefano Francaviglia (di Pisa), David Gay (UQAM), Tony Geramita (Queen’s), Mark Haskins (IHES), Rafael Herrera (Princeton), Alexander Ivrii (CRM), Thalia Jeffres (Michoacana), Barry Jessup (Ottawa), Rob Kirby (Berkeley), Benjamin Klaff (UQAM), John Klein (Wayne State), Joachim Kock (UQAM), Mar-garita Kraus (Regensburg), Steven Lu (Essen), Georges Maltsiniotis (Paris 7), Gideon Maschler (Toronto), Ion Mihai (Bucharest & Michigan State Univ.), Ramin Mohammadalikhani (CRM), Brendan Owens (McMaster), Saul Schleimer (Univ. of Illinois at Chicago), Margaret Symington (Georgia Tech.), Stephan Tillman (UQAM), Bogdan Vajiac (Indiana), S. Vidussi (Kansas State), Shicheng Wang (Beijing), Gregor Weingart (Bonn).

Geometric Group Theory Seminar

Responsible: Dani Wise Speakers: Inna Bumagin (McGill), Derrick Chung (McGill), Gabriel Indurskis (UQAM), Misha Kapovich (UC Davis), Raza Ali Kazmi (McGill), John Meier (Lafayette & Columbia), Igor Mineyev (IAS & UIUC), Bogdan Nica (McGill), Denis Serbin (Mc-Gill), Ralph Stohr (UMIST), Ted Turner (SUNY Albany), Dani Wise (McGill).

Séminaire CIRGET Junior

Responsible: Baptiste ChantraineSpeakers: Baptiste Chantraine (UQAM), Gabriel Chênevert (McGill), Alexandre Girouard (Montréal), Clément Hyvrier (Montré-al), Gabriel Indurskis (UQAM), Benjamin Klaff (UQAM), Joachim Kock (UQAM), Remi Leclercq (Montréal), Olivier Rousseau (Montréal), Stephan Tillman (UQAM).

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Mathematical Analysis laboratory At the same time classical and central to modern mathematics, analysis involves studying continuous systems from dynamical systems to solutions of partial differential equations and spectra of operators. The analysis laboratory was formed just one year ago. Currently the laboratory has 35 members working at ten different universities in Quebec, Ontario, France and the USA, with a particular concentration at Université de Montréal, Laval and McGill. Many of the main currents of modern analysis are studied by the group. Among the research subjects of the group, one fi nds conjectures on random waves and quantum chaos, Hamiltonian formalism in statistical mechanics far from equi-

librium, asymptotic properties of wave functions, Hilbert 16th problem and Hardy conjecture.

Besides four active seminars (McGill, Laval, Seminar in Non-linear Analysis and Dynamical Systems (Montréal), Analysis and Related Topics (joint colloquium series, University of Sher-brooke and Bishop’s University), members of the lab are cur-rently organizing a Year in Geometric and Spectral Analysis at CRM in 2003-2004 which will include twelve conferences and workshops.

DirecteurDmitry Jakobson (McGill)Pure mathematics, global analysis, spec-tral geometry, quantum chaos, harmonic analysis, eigenvalues and eigenfunctions.

Line Baribeau (Laval)Complex and functional analysis, Banach algebras, holomorphic iterations, discrete groups.

Abraham Boyarsky (Concordia)Dynamical systems

Francis Clarke (Claude Bernard, Lyon I)Nonlinear and dynamic analysis, control theory, calculus of variations.

Galia Dafni (Concordia)Harmonic analysis, partial derivative equations, complex variables.

Donald Dawson (Carleton)Probability, stochastic process.

Stephen Drury (McGill)Harmonic analysis, matrix theory.

Richard Duncan (Montréal)Ergodic theory, probability.

Richard Fournier (Dawson College)Probability, stochastic processes.

Marlène Frigon (Montréal)Nonlinear analysis, differential equa-tions, fi xed point theory, critical point theory, multivalent analysis.

Martin Gander (McGill)Domain decomposition, preconditio-ning.

Paul Gauthier (Montréal)Complex analysis, holomorphy, harmo-nicity, analytic approximation.

Pawel Gora (Concordia)Ergodic theory, dynamic systems, fractal geometry.

Frédéric Gourdeau (Laval)Banach algebras, cohomology, amenabi-lity, functional analysis.

Kohur GowriSankaran (McGill)Potential theory.

John Harnad (Concordia)Mathematical physics, classical and quantum physics, geometrical methods, integrable systems, group theoretical methods, random matrices, isomonodro-mic deformations, isospectral fl ows.

Antony R. (Tony) Humphries (McGill)Numerical analysis, differential equa-tions.

Vojkan Jaksic (McGill)Quantum mechanics, statistics, random Schrödinger operators.

Tomasz Kaczynski (Sherbrooke)Topological methods, Conley index, applications to dynamical systems.

Niky Kamran (McGill)Differential geometry, partial differential equations, mathematical physics.

Ivo Klemes (McGill)Harmonic analysis, trigonometric series.

Paul Koosis (McGill)Harmonic analysis.

Dmitry Korotkin (Concordia) Integrable systems, isomonodromic deformations, classical and quantum gravity, Frobenius varieties.

Javad Mashreghi (Laval)Complex analysis, harmonic analysis, Hardy spaces.

Nilima Nigam (McGill)Applied analysis, numerical methods in electromagnetism.

Yiannis Petridis (CUNY, Lehman College)Automorphic Forms and Spectral Theory. L-Functions, Quantum chaos.

M e m b e r s o f t h e M a t h e m a t i c a l A n a l y s i s l a b o r a t o r y M e m b e r s o f t h e M a t h e m a t i c a l A n a l y s i s l a b o r a t o r y

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Iosif Polterovich (Montréal)Complex analysis, functional analysis, spectral theory, potential theory, Jensen measures.

Thomas Ransford (Laval)Complex and harmonic analysis, func-tional analysis and theory of operators, spectral analysis, potential theory.

Dominic Rochon (UQTR)Numbers, analysis, dynamic complexes.

Jérémie Rostand (Laval)

Complex analysis, experimental math-ematics.

Christiane Rousseau (Montréal)Dynamical systems, bifurcations, qualita-tive theory, polynomial systems, analytic invariants, integrable systems.

Dana Schlomiuk (Montréal)Global analysis, dynamical systems, sin-gularities, bifurcations, algebraic curves, primary integral.

Georg Schmidt (McGill)Control of partial differential equations.

Ron Stern (Concordia)

Functional analysis and theory of opera-tors, linear and non-linear systems, non-smooth analysis, stability, optimal order.

John Toth (McGill)Spectral theory, semi-classical analy-sis, micro-local analysis, Hamiltonian mechanics.

Samuel Zaidman (Montréal)

Highlights of the activities of the laboratory and of its members 2003-2004 Highlights of the activities of the laboratory and of its members 2003-2004 Highlights of the activities of the laboratory and of its members 2003-2004

• J. Rostand (Laval) have recently become members of the lab.• A member of our lab, Line Baribeau (Laval), has been promoted to full professor with effect from June 1, 2004. Many congratula-

tions!• Some of the activities of the lab are described on the “Analysis in Quebec” web page, http://www.math.mcgill.ca/jakobson/analy-

sish/analysis.html• Conference in Classical Analysis in Honor of Paul Koosis (October 23-26, 2003). This conference was organized by G. Dafni

(Concordia), D. Jakobson (McGill), J. Mashreghi (Laval).

Conference in Classical Analysis in Honor of Paul Koosis

Invited Speakers:David Drasin (NSF), Positive harmonic functions in T-automorphic domains John Garnett (UCLA), Analytic Capacity, Cauchy Integrals, Bilipschitz Maps and Cantor SetsVictor Havin (St. Petersburg & McGill), Variations on a theme by Beurling and Malliavin Walter Hayman (Imperial College), ABC, Waring and Fermat for functionsPeter Jones (Yale), Brownian Motion and Bounded Square Functions: Joint Work with Paul MullerJean-Pierre Kahane (Orsay), Old and new results on partial sums of Fourier seriesIvo Klemes (McGill), Extension of a lemma of Gohberg and KreinPaul Koosis (McGill) A lemma about being analytic. Applications of the same (if time permits)Javad Mashreghi (Laval), Entire function of exponential type, binomial sums and Banach algebrasRobert Milson (Dalhousie), On the abstract defi nition of a differential operatorFedya Nazarov (Michigan State), Sharp bound for the area of the set of positivity of a harmonic function with prescribed number of sign changes on the boundaryLouis Nirenberg (Courant), Distance function to the boundary and Hamilton-Jacobi equationsHenrik L. Pedersen (Royal Veterinary and Agricultural University), Entire functions and logarithmic sumsTom Ransford (Laval), Cyclic vectors in the Dirichlet spaceMisha Sodin (Tel Aviv), Growth, zeroes, and area estimates. Variations on the theme Sergey Treil (Brown), The Operator Corona Problem and geometry of holomorphic vector bundlesSasha Volberg (Michigan State), Applications of nonhomogeneous Harmonic Analysis: capacities, perturbations of unitary operators, dynamicsMichael Wilson (Vermont), Some Littlewood-Paley resultsReem Yassawi (Trent), Asymptotic randomisation of measures by Cellular Automata on Sofi c Shifts

Members of the Mathematical Analysis laboratory - continued

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Analysis - Université de Montréal

Responsible: Paul Gauthier (Montréal).Speakers: Richard Fournier, (CRM, Montréal, & Collège Dawson).

Analysis - Université Laval

Responsible: Javad Mashreghi (Laval). Speakers: Ariel Blanco (Laval), Frédéric Gourdeau (Laval), Abdessamad Safoui (Marrackech).

Analysis and Related Topics

Responsibles: Tomasz Kaczynski (Sherbrooke), Tilak Bhattacharya (Bishop’s), François Dubeau (Sherbrooke), Madjid Allili (Bish-op’s).Speakers: André Bandrauk (Sherbrooke), Tilak Bhattacharya (Bishop’s), Michel Delfour (Montréal), Marlène Frigon (Montréal), Wieslaw Krawcewicz (Alberta), Konstantin Mischaikow (CDSNS, Georgia Institute of Technology), Christiane Rousseau (Mon-tréal), Alina Stancu (Montréal), Michel Virgilio (Sherbrooke), Lourdes Zubieta (Bishop’s).

Seminar in Nonlinear Analysis and Dynamical Systems

Responsibles: Pietro-Luciano Buono (CRM), Alina Stancu (Montréal). Speakers: Joan Carles Artés (Autonoma de Barcelona (Spain)), Pietro-Luciano Buono (Montréal), Michael Gage (Rochester), Alexan-dre Girouard (Montréal), A. El Khalil (Montréal), François Lalonde, (Montréal), Konstantin Mischaikow (Georgia Tech), Alexei Penskoi (Montréal), Christiane Rousseau (Montréal), Dimiter Vassilev (UQAM), Elisabeth Werner (Case Western Reserve).

McGill Analysis

Responsible: Dmitry Jakobson (McGill).Speakers: Emily Dryden (Dartmouth), Pengfei Guan (McMaster), Daniel Grieser (Bonn), Victor Ivrii (Toronto), Michael Levitin (Heriot-Watt), Stanislav Molchanov (North Carolina), Fedya Nazarov, Alexander Pushnitski (Loughborough), Philong Thanh (McGill), Ignacio Uriarte-Tuero (Yale).

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LaCIM is a research laboratory of the Université du Québec à Montréal, which was officially established in 1989. Its research activities concentrate on enumerative algebra, algebraic combi-natorics, computer science and their applications to other scien-tific domains, such as the analysis of algorithms, statistical me-chanics and computational biology. Since 2002 LaCIM is one of the eight research laboratories of the CRM.

Research areas

Discrete mathematics has lately become an important field of practical research, witness the new heading in Mathematical Re-views 05E of algebraic combinatorics with subheadings indicat-ing interactions with the newest areas of mathematics, such as group representations, quantum groups, discrete algebraic ge-ometry, special functions. Combinatorics benefits from the re-vival of the concrete computational aspect in mathematics after decades of abstract structuralism. Algebra is enriched in a fun-damental manner by combinatorics, as the commutative algebra book by Eisenbud demonstrates, highlighting constructive geo-metric methods. Moreover, combinatorics applies to computer sciences (theory of automata, analysis of algorithms), to statisti-cal physics (computation of configuration spaces and of critical exponents, discrete models), bio-informatics (combinatorics of words applied to genomic sequences). The youth, dynamism, utility and applicability of this research domain are highlighted in the modern world, where discrete structures (trees, graphs, permutations) are more and more present in communications, networks and research engines, of which the use is growing ex-ponentially in this 21st century.

The researchers

The laboratory is comprised of twelve principal researchers, ten of them professors at UQAM, one at McGill and one at Univer-sité de Montréal; of ten associate members and four associated in North America, one in Chile and two in Europe. Notably, Christophe Reutenauer (regular member) and Nantel Bergeron (associate member, York University) hold Canadian research chairs. A team of four LaCIM members is supported by a grant from FCAR. André Joyal, past member of LaCIM and current member of CIRGET, is involved in several activities at LaCIM, both formal and informal. LaCIM is the largest research group in combinatorics in Canada and is known worldwide in its field. The UQAM team has contributed to the emergence and estab-lishment of combinatorics as a mathematical discipline. For ex-ample, several LaCIM members have played and continue to play an important role in the organization of the international colloquium Séries formelles et combinatoire algébrique, which is bilingual and is held yearly, alternately in Europe and North America. Its success is without question.

Research activities at LaCIM

A. Joyal enriched the counting theory of Polya by including the theories of group representations and symmetric functions. Un-der the name of theory of species, this theory marked the emer-gence of the UQAM combinatorics group about twenty years ago. From that time research has diversified greatly at LaCIM: a) classical enumerative combinatorics and its applications (count-ing of discrete configurations and planar maps); b) algebraic combinatorics; c) theoretical computer science; d) bio-informat-ics.

LaCIM (Laboratoire de combinatoire et d’informatique mathématique)

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DirecteurChristophe Reutenauer (UQAM)Algebraic combinatorics, non-commu-tative algebra, automata, codes, free algebras.

Robert Bédard (UQAM)Representations of fi nite groups, Lie theory.

Luc Bélair (UQAM)Mathematical logic, model theory.

Anne Bergeron (UQAM)Bio-informatics.

François Bergeron (UQAM)Combinatorics, algebras, representations of fi nite groups.

Nantel Bergeron (York Univ.)Applied algebra

Pierre Bouchard (UQAM)Commutative algebra, algebraic geo-metry and combinatorics. Srecko Brlek (UQAM)Combinatorics of words, algorithmics.

Cedric Chauve (UQAM)Enumerative combinatorics, trees, bio-informatics.

Sylvie Hamel (Montréal)Bio-informatics and algorithms, language and automaton theory, algebraic combi-natorics.

André Joyal (UQAM)Algebraic topology, theory of categories.

Gilbert Labelle (UQAM)Enumerative combinatorics, analysis.

Jacques Labelle (UQAM)Combinatorics, topology.

Louise Laforest (UQAM)Data structures, combinatorics, asymp-totical analysis, quaternary trees.

Pierre Leroux (UQAM)Enumerative and algebraic combinato-rics.

Vladimir Makarenkov (UQAM)Computational biology, mathematical classifi cation.

Denis Thérien (McGill)Theory of complexity of computation, logic, combinatorics, probability.

Timothy Walsh (UQAM)Algorithmics, enumerative combinato-rics, graphs.

Highlights of the activities of the laboratory and of its members 2003-2004Highlights of the activities of the laboratory and of its members 2003-2004Highlights of the activities of the laboratory and of its members 2003-2004

M e m b e r s o f t h e L a C I MM e m b e r s o f t h e L a C I M

Collaborations between members

As mentioned last year, the number of collaborations between LaCIM members, which demonstrates the dynamism and cohesion of the group, were numerous: Bergeron-Chauve in bio-informatics (with a new postdoctoral collaborator, Annie Château); Brlek-Hamel-Reutenauer in combinatorics of words; Leroux-Labelle in theory of categories; Brlek-Labelle in pattern recognition; Laforest-Labelle in data structures; Bergeron-Reutenauer in algebraic combinatorics.

Visitors

LaCIM hosted several visitors: Juhani Karhumäki (Turku), invited by Srecko Brlek. David Liben-Nowell (MIT) in bio-informa-tics, collaborators of Cédric Chauve and Anne Bergeron; Guillaume Fertin and Guillaume Blin (Nantes), collaborators of Cédric Chauve in bio-informatics; Philippe Caldero (Lyon) and Volker Heiermann (Berlin), collaborators of Robert Bédard; Valérie Berthé (Montpellier), Jean-Pierre Borel (Amiens), Michel Koskas (Amiens), Michel Mendès France (Bordeaux), and Jean Berstel, invited by Srecko Brlek and Christophe Reutenauer, for collaborative work in the combinatorics of words; Florent Hivert (Marne la Vallée and Moscow), who collaborates with François Bergeron and Nantel Bergeron; in May 2004, a working group in combinatorics of words, led by Srecko Brlek, will bring together Sébastien Ferenczi and Julien Cassaigne (Marseille), during ten days on the Montréal-Vancouver train; Mark Haiman (Berkeley) and Adriano Garsia (San Diego), invited by François Bergeron; Sergey Fomin, invited by François Bergeron and Robert Bédard fpr the ACFAS Congress in May 2004.

• Gilbert Labelle was a member of the scientifi c committee of scientifi que of the FPSAC conference held in Vancouver in June 2004.• Denis Thérien holds a James McGill Chair at McGill University (2002-2009).• Christophe Reutenauer holds a Canada Research Chair in Combinatorial Algebra and Mathematical Computing (2001- 2008).

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Séminaire de combinatoire et informatique mathématique

Responsibles: Cedric Chauve & Pierre Leroux (UQAM).Speakers: Robert Bédard (UQAM), François Bergeron (LaCIM-UQAM), Nantel Bergeron (York), Jean Berstel (Marne-la-Vallée), Valérie Berthé (LIRMM), Riccardo Biagioli (LaCIM-UQAM), Jean-Pierre Borel (Limoges), Annie Château (LaCIM-UQAM), Sara Faridi (UQAM), Guillaume Fertin (IRIN, Nantes), Samuel Fiorini (Univ. libre de Belgique & GERAD-HEC), Adriano Garsia (Univ. de la Californie à San Diego), Tony Geramita (Queen’s & Genova), Mark Haiman (Univ. de la Californie à Berkeley), Sylvie Hamel (Montréal), Michel Koskas (LARIA (Amiens)), Jacques Labelle (UQAM), Pierre Leroux (UQAM), Vadim Lioubimov, Pierre Mathieu (Laval), Peter McNamara (UQAM) Karen Meagher (Ottawa), Michel Mendès-France (Bordeaux), Igor Pak (MIT), Simon Plouffe, Étienne Rassard (MIT), Mercedes Rosas (LaCIM-UQAM), Bruno Salvy (INRIA), Mark Skandera (Dartmouth College), Benjamin Steinberg (Herzberg Labs, Carleton), Adrian Vetta (McGill), Timothy Walsh (LaCIM-UQAM).

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Applied Mathematics Laboratory

Applied and Computational Mathematics is a very active area of research with a long tradition as well as many young faculty members in the greater Montreal area. With modern comput-ing equipment, it has become possible to simulate problems and compute solutions which one was only able to dream of a few decades ago: this has been a tremendous driving force in recent developments in applied and computational mathematics.

The laboratory members work in a wide range of applications (fl uids, solids, physics, biology etc.) using a wide variety of tools (optimisation, numerical analysis, dynamical systems, etc). The objective of the new applied math laboratory is to further en-

courage scientifi c exchanges both amongst its members and outside group. It is characterized by the intensity of its multi-disciplinary collaborations, with all its members working on the development of mathematical models and numerical methods for applications to science and engineering. The laboratory has two regular seminars running during the academic year, a weekly applied mathematics seminar and a biweekly computational sci-ence and engineering seminar. It also supports postdoctoral fel-lows and summer students as well as Canadian and international visitors.

DirecteursAnne Bourlioux (Montréal)Modeling, numerical simulation in turbu-lent combustion.

Martin Gander (McGill)Domain decomposition, preconditio-ning.

Jacques Bélair (Montréal)Dynamical Systems in physiology.

Paul Arminjon (Montréal)Numerical methods in fl uid mechanics.

André Bandrauk (Sherbrooke)Quantum chemistry.

Peter Bartello (McGill)Turbulence, CFD.

Michel Delfour (Montréal)Control, optimization, design, shells, cal-culus, biomechanics.

Tony Humphries (McGill)Numerical analysis, differential equa-tions.

Sherwin A. Maslowe (McGill)Asymptotic methods, fl uid mechanics.

Nilima Nigam (McGill)Applied analysis, numerical methods in electromagnetism.

Georg Schmidt (McGill)Control of partial differential equations.

Jian-Jun Xu (McGill)Asymptotics and Numerical Analysis, Nonlinear PDEs material science.

Jean-Paul Zolésio (INRIA)Control, optimization.


Members of the Applied Mathematics LaboratoryMembers of the Applied Mathematics Laboratory

The members of the applied mathematics laboratory are very active in both research and training, supervising a large number of graduate students and post-doctoral fellows. One characteristic of this laboratory is the sustained collaboration of its members with researchers in other fi elds: for instance, Nilima Nigam is a member of RQMP (Regroupement Quebecois des materiaux de pointe), Martin Gander and Michel Delfour are members of GIREF, Anne Bourlioux collaborates with computer scientists and mechanical engineers in an industrial project sponsored by Mitacs, while Peter Bartello, Andre Bandrauk, and Sebius Doedel hold positions completely or partly outside mathematics departments.

The core activity of the laboratory is the weekly applied mathematics seminar that takes place on Mondays at McGill. It was organized this year by Tony Humphries, who succeeded at lining up 24 speakers covering a very wide range of interesting topics in applied mathematics. The laboratory was also involved in organizing and sponsoring the bi-weekly Computational Science and Engineering Seminar at McGill, organized this year by Luca Cortelezzi, (Mechanical Engineering, McGill). Several of the laboratory visitors, including A. Fortin (Laval), V. Dolean (Ecole Polytechnique, Paris), A. St Cyr (NCAR, Boulder), A. Spence (Bath), spoke in the CSE seminar.

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S e m i n a r s 2 0 0 3 - 2 0 0 4 A p p l i e d M a t h e m a t i c s L a b o r a t o r yS e m i n a r s 2 0 0 3 - 2 0 0 4 A p p l i e d M a t h e m a t i c s L a b o r a t o r y

Applied Mathematics

Responsibles: Michel C. Delfour (CRM), Antony R. (Tony) Humphries (McGill), Paul Tupper (McGill), José Manuel Urquiza (CRM).Speakers: Jean-Pierre Aubin (Paris-Dauphine), Stefanella Boatto (McMaster), Stéphane Dellacherie (CRM), Selim Esedoglu (UCLA), Guido Kanschat (Heidelberg), Olivier Lafi tte (Paris 13, CEA - Saclay), M. Laforest (École Polytechnique Montréal), Claude LeBris (CERMICS-ENPC), Tony Lelièvre (CRM), André Longtin (Ottawa), Sherwin Maslowe (McGill), Alexander Mel-nikof, (Alberta), Peter Monk (Delaware), Arian Novruzi (Ottawa), Robert Owens (Montréal), Jan Sieber (Bristol), David Straub (AOS - McGill), Andrea Toselli (ETH Zürich), Thomas P. Wihler (Minnesota), Dongbin Xiu (Princeton).

Besides those regular activities, the laboratory organized the fi rst edition of what is to become a yearly activity in numerical analysis, aimed at the Quebec and surrounding community - the Montreal Scientifi c Computing Days. This fi rst edition was a great success as it attracted more than 70 registered participants from Quebec and Ontario. It was a 2-day (weekend) activity, with two main speakers lecturing on recent developments in scientifi c computing at a level accessible to advanced graduate students, along with oral and poster presentations by local, junior researchers. One ingredient of the success was the prestige of the two main speakers, E. Hairer (Geneva) and E. Darve (Stanford).

The laboratory members were also hosts to a number of scientifi c visitors. E. Hairer is one of them: the Scientifi c Computing days were organized around his visit, as well as his conference at the CRM-ISM colloquium. Another long term visitor sponsored in part by the laboratory was Bob Russell (SFU) who spent the fall at McGill while being on sabbatical leave. He also gave one colloquium, as well as two seminars, and had many interactions with several laboratory members.

The laboratory members are also very visible at the national level in applied and industrial mathematics. André Bandrauk was elec-ted a Fellow of the American Association for the Advancement of Science in October 2003 and Michel Delfour was a John Simon Guggenheim Memorial fellow for 2003-4. Several members were actively involved in the joint SIAM-CAIMS annual meeting in Montreal, June 2003: Anne Bourlioux as a member of the scientifi c organizing committee, Michel Delfour as a plenary lecturer, Andé Bandrauk, E. Doedel, Martin Gander, Tony Humphries, Nilima Nigam, and Paul Tupper as mini-symposia organizers or speakers. A. Bandrauk was on the organizing committees for the First Canadian Workshop on Ultrafast Dynamic Imaging at Orford in October 2003, and the NRC Ottawa workshop on Dynamic Imagery. Tony Humphries was a deputy director of the CRM.

For the forthcoming year, Anne Bourlioux has just been elected to the board of directors of CAIMS, and several members of the lab are involved in organizing and participating in various symposia during the 2004 CAIMS annual meeting (joint with CMS, to be held in Halifax): J. Belair (who has just joined the lab), T.Humphries, E. Doedel, M.Gander.

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Mathematical Physics Laboratory

Directeur John Harnad (Concordia)Mathematical physics, classical and quantum physics, geometrical methods, integrable systems, group theoretical methods, random matrices, isomonodro-mic deformations, isospectral fl ows.

Syed Twareque Ali (Concordia)Coherent states, wavelets, quantization techniques, harmonic analysis, Wigner functions.

Marco Bertola (Concordia)Axiomatic quantum fi eld theory, inva-riant theory of discrete groups, random matrices, isomonodromic deformations.

Chris Cummins (Concordia)Group theory applications to mathemati-cal physics, modular functions and their relation to sporadic groups.

Alfred Michel Grundland (UQTR)Symmetry of differential equations in physics.

Richard L. Hall (Concordia)Quantum mechanics, geometry, spectral inversion, many-body problem.

Jacques Hurtubise (McGill)Algebraic geometry, integrable systems, gauge theory, moduli spaces.

Véronique Hussin (Montréal)Quantum mechanics, differential equa-tions, Lie groups, Lie algebras, group deformations, supersymmetries.

Dimitry Jakobson (McGill)Quantum Chaos, Spectral Geometry, Harmonic Analysis.

Vojkan Jaksic (McGill)Mathematical physics, quantum statis-tical mechanics, random Schrodinger operators.

Niky Kamran (McGill)Differential Geometry, partial differen-tial equations, mathematical physics.

Dmitry Korotkin (Concordia) Integrable systems, isomonodromic deformations, classical and quantum gravity, Frobenius varieties.

Fançois Lalonde (Montréal)Symplectic topology and geometry, global analysis, infi nite dimensional transformation groups.

Jean LeTourneux (Montréal)Symmetry properties os systems, special functions.

Pierre Mathieu (Laval)Conformal fi eld theory, classical and quantum integrable systems, affi ne Lie algebras.

Jiri Patera (Montréal)Applications of group theory,quasi-crys-tals, Lie algebras.

Yvan Saint-Aubin (Montréal)Conformal fi eld theory, statistical me-chanics, 2-dimensionalphase transition model.

John Toth (McGill)Partial differential equations, mathematical physics and spectral theory.

Luc Vinet (McGill)Symmetric properties of systems, special functions.

Pavel Winternitz (Montréal)Methods of group theory in physics, nonlinear phenomena, symmetries of difference equations, superintegrability.

M e m b e r s o f t h e M a t h e m a t i c a l P h y s i c s M e m b e r s o f t h e M a t h e m a t i c a l P h y s i c s

The mathematical physics group is one of the oldest and most active within the CRM. It consists of 20 regular members, all full time faculty members attached permanently to fi ve differ-ent Quebec Universities. (Eight of these are also associated with the CRM Analysis Laboratory or with CIRGET, and one with CICMA). In addition, the Lab includes two attachés de recher-ches, numerous postdoctoral fellows (currently 19, of whom 11 are concurrently attached to one of the other laboratories men-tioned ) and a large number of graduate students (currently over 40, about 1/3 of whom are working with members attached also to the CIRGET or Analysis laboratories).

The group carries out research in several of the most signifi cant areas of current interest in mathematical physics, such as: Coher-ent nonlinear systems in fl uids, optics and plasmas; classical and quantum integrable systems; spectral theory of random matri-ces; percolation phenomena; conformal fi eld theory; quantum statistical mechanics; spectral and scattering theory of random Schrödinger operators; quasi-crystals; relativity; spectral trans-form methods; asymptotics of eigenstates; foundational ques-tions in quantization (stochastic and geometric quantization); coherent states; supersymmetry; symmetry analysis of P.D.E.’s; symmetries and integrability of difference equations; representa-tion theory of Lie groups and quantum groups; and the math-ematical structure of classical and quantum fi eld theories.

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Stéphane Durand (Collège Edouard-Montpetit)Classical and quantium physics, mathe-matical physics, simmetries, parasuper-symmetries, fractional supersymmetries, KdV, quantum mechanics, relativity.

Carolyne Van Vliet (Miami)Non-equilibrium statistical mechanics, fl uctuations and stochastic processes, quantum transport in condensed matter, electronic behavior in submicron quan-tum devices.


S e m i n a r s 2 0 0 3 - 2 0 0 4 M a t h e m a t i c a l P h y s i c s L a b o r a t o r yS e m i n a r s 2 0 0 3 - 2 0 0 4 M a t h e m a t i c a l P h y s i c s L a b o r a t o r y

Vasile Brinzanescu (Bucharest) (May 10 - 24 2004)

G. Cassinelli (Genova) (Sept. 8 - 20 2003)

S. De Bievre (Lille) (Sept. 5 - 20, 2003)

V. Dorodnitsyn (Moscow) (Jan. 17 - Feb. 8, 2004) )

Miroslav Englis (Sept. 26 - Oct. 14 2003)

Bertrand Eynard (Saclay) (Feb. 2 - 12, April 2004)

V. Enolskii, (Kiev) (May 22-28, 2004)

D. Grieser (Berlin) (Aug. 20 - Sept. 5, 2003, June, 2004)

Andrei Kapaev (St. Petersburg) (Mar. 1 - 31, 2004)

A. Klimyk (Ukrainian Acad. Sciences, Kiev) (18 Nov - 12 Dec. 2003)

A. Kokotov (St. Petersburg) (Jan. 1 - May 31 2004)

Decio Levi (Rome) (Nov. 23 - Dec. 9 2003). Luigi Martina (Lecce) (July, Aug. 2003))

M e m b e r s o f t h e M a t h e m a t i c a l P h y s i c s l a b o r a t o r yM e m b e r s o f t h e M a t h e m a t i c a l P h y s i c s l a b o r a t o r y

The regular CRM Mathematical Physics seminar series was continued throughout the academic year, with weekly talks given both by invited visitors and local members of the Lab, including postdoctoral fellows and some graduate students near to completion of their doctorates. In addition, a second “working seminar in mathematical physics” was organized by V. Jaksic at McGill, with active partcipation by members of the Analysis Lab. (A list of the titles for these two series’ may be found at the web sites: http://omega.crm.umontreal.ca/~physmath/calendriers/seminaire_fr.html and: http://www.math.mcgill.ca/jaksic/wsmp.html)

V. Matveev (Dijon) (Feb. 29 - April 10 2004)

Maung Min-Oo (McMaster) (Aug. 2003)

Yousuke Ohyama (Osaka) (Mar. 4 - Apr. 2, 2004)

Shoji Okumura (Osaka) (Feb. 29 - Mar. 19, 2004)

E. Previato (Boston) (Mar. 22-28, 2004)

I. Rivin (Temple) (visiting Jakobson)

Miguel A. Rodriguez (Madrid) (July 2003)

Z. Rudnick (Tel-Aviv) (Apr. 20. - May 10, 2004)

Misha B. Sheftel (Istanbul) (Jan. 2004 - Feb. 2004, Summer 2004)

A. Soshnikov (UC Davis) (Nov. 20 - 24)

Zora Thomova (SUNY) (Oct. 10-14, Nov. 26-30 2004)

Steve Zelditch (Johns Hopkins) (Nov. 2 - 11, 2003, Jan. 5 - 10, 2004). 5 au 10 janvier 2004).

The members of the Laboratory maintain active ties and ongoing collaborations with other researchers from centers in mathematical physics around the world. The list of scientifi c visitors to the laboratory this academic year included:

Stéphane Durand, lecturer at the Physics Department of Université de Montréal received the “Petit Nobel de pédagogie” from the Department.

• Jiri Patera was awarded the joint CRM-CAP Prize in Mathematical Physics for 2003-2004.• Several members of the laboratory (Vojkan Jaksic, Niky Kamran, John Toth) were organizers for this year’s CRM thematic year

on Geometry and Spectral Analysis.

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Statistics Laboratory

Statistics is central to many endeavours in society. Whether it be through surveys from sampling, clinical trials to study various biomedical treatments or experimental designs in agriculture or industry, statistical methodology can be found everywhere in science. Recently, statistics has been undergoing a revolution in its techniques and its approaches. This revolution has been driven by the need to analyze very large data sets, data with more complex structure, and by the advent of powerful computers. For example, statistical methodology is now addressing problems whose structure is more complex, such as brain images or genome data and new methodology is developed for large data sets. Data-

mining is one of the tools used. The laboratory aims at structuring the Québec community to engage with this revolution at a time of an important renewal of academic personnel. This structure allows the Québec community to benefi t from a new pan-Cana-dian program in analysis of complex data organized by the three Canadian mathematics institutes. The laboratory is composed of the leaders of the Québec school of statistics who work on subjects such as statistical learning and neuronal networks, survey sampling, analysis of functional data, statistical analysis of images, dependence structures, Bayesian analysis, analysis of time series and fi nancial data, as well as resampling methods.

Directeur Christian Léger (Montréal)Resampling methods, adaptive estima-tion, model selection, robustness, ap-plications in data mining.

Jean-François Angers (Montréal)Desision theory, Bayesian statistics, robustness with respect to prior informa-tion, function estimation.

Yoshua Bengio (Montréal)Statistical learning algorithms, neural networks, nucleus models, probabilistic models, data mining, applications in fi -nance and statistical language modelling.

Martin Bilodeau (Montréal)Multivariate analysis, decision theory, asymptotic methods.

Yogendra Chaubey (Concordia)Sampling, linear models, resampling, sur-vival analysis.

René Ferland (UQAM)Probability, statistic processes, applica-tions to mathematical fi nance.

Christian Genest (Laval)Multidimensional data analysis, depend-ence measures, nonparametric statistics, decision theory, applications in actuarial science, fi nance and psychology.

Nadia Ghazzali (Laval)Multidimensional data analysis, neural networks and genetic algorithms, applica-tions in astrophysics and biostatistics.

Brenda MacGibbon (UQAM)Mathematical statistics, decision theory, biostatistics.

François Perron (Montréal)Decision theory, multidimensional data analysis, Bayesian statistics.

Jim Ramsay (McGill)Functional data analysis, smoothing and nonparametric regression, curve registra-tion.

Bruno Rémillard (HEC Montréal)Probability, empirical processes, time se-ries, nonlinear fi ltering, applications in fi nance.

Louis-Paul Rivest (Laval)Linear models, robustness, directional data, sampling, applications in fi nance.

Roch Roy (Montréal)Time series analysis, predictive methods, applications in econometrics and epide-miology.

David B. Wolfson (McGill)Changepoint problems, survival analysis, Bayesian statistics, optimal design, appli-cations in medicine.

Keith J. Worsley (McGill)Statistics of brain mapping, geometry of random images in medicine and astro-physics.

M e m b e r s o f t h e S t a t i s t i c s L a b o r a t o r yM e m b e r s o f t h e S t a t i s t i c s L a b o r a t o r y

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News and highlights

Many good news originate from this laboratory. The most important one is that Louis-Paul Rivest was awarded a senior Canada Research Chair (CRC) in statistical sampling and data analysis. This is one of the fi rst CRC in statistics. As a recognition of excellence throughout his career, Keith Worsley has been nominated James McGill Professor. Moreover, he just received the Statistical Society of Canada’s (SSC) Gold Medal awarded to a senior statistician for his substantial contributions to statistics. Bruno Rémillard is one of the authors of the paper selected as the winner of the Canadian Journal of Statistics award for 2003. Yoshua Bengio is a member of the scientifi c committee of the prestigious conference entitled NIPS 2004. Christian Léger is a member of NSERC’s grants selection committee in statistics. He is also the Chair of the local organizing committee of the 2004 Annual Meeting of the SSC which took place at CRM while Christian Genest chaired the scientifi c committee. Jean-François Angers completed his mandate on the SSC Executive as Public Relations Offi cer while Jim Ramsay ended his mandate as Past President.

Activities

The laboratory continued organizing the CRM-ISM Statistics Colloquium that began Winter 2003. In February, Jim Ramsay gave a two-day workshop on functional data analysis. Despite a lack of time for proper advertising, this activity attracted 39 participants, including many students. This workshop covered many topics of functional data analysis, from the basics to some advanced issues. The most important scientifi c activity of the laboratory this year is, without a doubt, DeMoSTAFI (Dependence Modelling: Theory and Applications in Finance and Insurance) which took place at Université Laval in May 2004. This three-day international confer-ence attracted 112 participants from 18 countries. Organized by Christian Genest, it brought together the best researchers working on copulas, including nine invited speakers. A special issue of the most important actuarial journal, Insurance: Mathematics and Economics, will be devoted to fi nance and actuarial papers presented at the conference. Moreover, a special issue of the Canadian Journal of Statistics will be devoted to papers with a more statistical fl avour that were also presented at that conference. This impact of this activity will therefore be felt well beyond the laboratory and will further improve CRM’s image with the Canadian statistical community.

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Seminars 2003-2004 - Stat ist ics laboratory Seminars 2003-2004 - Stat ist ics laboratory

Statistics McGill

Responsibles: George P.H. Styan, Keith J. Worsley (McGill).Speakers: Mirza I. Beg (Hyderabad & Concordia), Felix Carbonell (Institute for Cybernetics, Mathematics & Physics (Havana, Cuba)), Moo K. Chung (Wisconsin-Madison), Nick Lange (Harvard Medical School), Cyr Émile M’lan (Hospital of Sick Children (Toronto)), Sumitra Purkayastha (Indian Statistical Institute), Jonathan Taylor (Stanford), Yongge Tian (McGill & Queen’s).

Statistics Université Laval

Responsible: Louise Chamberland (Laval).Speakers: Gülhan Alpargu (Massachusetts), David R. Bellhouse (Western Ontario), Cathy Blanchette (Hôpital Saint-Sacrement du centre hospitalier universitaire de Québec), Christian Boudreau (Medical College of Wisconsin), Inna Bumagin (McGill), Judy-Anne Chapman (Women’s College Hospital, Toronto), Aurore Delaigle, (California at Davis), Jean-Pierre Dion (UQAM), Charles Dugas (Montréal), Anne-Catherine Favre, (Inst. Natl. de la recherche scientifi que - ETE), Marc Fredette (Waterloo), Christian Genest (Laval), El Hadji Guèye (Laval), Serge Guillas (Chicago), Aurélie Labbe (Waterloo), Chantal Labbé (Waterloo), Guy Lacroix (Laval), Fabrice Larribe (McGill), Robert Nadon (McGill), Théophile Niyonga (Centre hospitalier universitaire de Sherbrooke), François Pageau (SNC-Lavallin), Roger Pradel (Centre d’ecologie fonctionnelle et évolutive de Montpellier), Jean-François Quessy (UQTR), Meriem Saïd (Laval), Abdessamad Saïdi (Montréal).

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PhysNum

PhysNum has the particularity of having been created at the CRM and a great part of its research activity takes place within its walls. This particularity, which contributes to the Centre’s visibility within the fi eld of applied mathematics, explains its relatively small size compared to the extent of its collaborations within the milieu of brain imaging in Montréal and elsewhere. PhysNum collaborates with Regroupement Neuro-imagerie Québec (headed by Y. Joanette and J. Doyon), GRENE (headed by F. Lepore, Psychology, Univ. de Montréal), and the group Imagerie Quantitative of INSERM’S Unité 494 in Paris (headed by H. Benali). The greater part of fi nancial resources areinvested on student researchers at the CRM. Our research with these groups pertains to mathematical imaging, essentially in medi-cine, within the following themes:

• Analysis and modeling of wavelets (thermodynamic formal-ism, graphic models);

• Fractal and multifractal analysis (analysis of materials, angio-genesis, turbulent signals)

• Probabilistic approach to the resolution of inverse problems (maximum entropy inference, independence graphs)

These tools are used in a number of clinical and cognitive do-mains detailed below. The different teams centred on neurol-ogy mentioned above are interested in the development of “ fi ne methods” within their particular research domains and are thus interested in pursuing a longterm relationship

DirecteurBernard Goulard (Montréal)Brain imaging.

Alain Arnéodo (ENS, Lyon)Fractal and wavelets.

Habib Benali (INSERM, CHU Pitié-Salpêtrière, Paris)Brain imaging.

Line Garnero (CNRS UPR 640-LENA, Paris)Magneto-encephalography.

Frédéric Lesage (ART Recherches et Technologies Avancées Inc.)Conformal theory, integrable systems, inverse problems.

Jean-Marc Lina (Montréal)Wavelets, statistical modeling and brain imaging, algorithms for statistical learn-ing.

Fahima Nekka (Montréal)Fractal analysis.

Keith J. Worsley (McGill)Geometry of random images in medicine and astrophysics.

M e m b e r s o f t h e P h y s N u m M e m b e r s o f t h e P h y s N u m

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Maximum d’Entropie et inférence en Magnéto-Encéphalo-Graphie (MEG)

L’éude de l’inférence par maximum d’entropie pour des modèles de mixtures a été poursuivie dans le cadre du problème d’estimation de sources cérébrales en magnéto-encéphalographie. Mise au point dans le travail (Cécile Amblard, Ervig Lapalme, Jean-Marc Lina, (2004)), le maximum d’entropie sur la moyenne (MEM) ayant une correspondance avec le formalisme Bayesien; le travail a essentiellement porté sur la version ‘Bayesien empirique’ du MEM. Ce développement original du MEM permet ainsi de mieux contrôler la loi de référence présente dans le formalisme du MEM. Évalué sur des simulations en MEG à temps fi xe, le formalisme continue de démontrer sa stabilité et sa robustesse dans l’estimation des sources dipolaires distribuées (10 000 sources) sur le cortex (Ervig Lapalme, Jean-Marc Lina, Jérémie Mattout, (2004)). Dernière étape dans ce volet de recherche, l’estimation des séries temporelles en MEG et l’évaluation des performances du MEM sur des données réelles sont actuellement en cours et font l’objet de la rédaction d’un article (Ervig Lapalme, Jean-Marc Lina, Bernard Goulard, (2004)).

Modélisation et inférence entropique sur des arbres multi-échelles

Suite à un séjour de Jacques Levy-Vehel (INRIA, Fr.), PhysNum, a accueilli une de ses étudiantes de DEA qui a initié l’étude du principe de maximum d’entropie sur des arbres multi-échelles en ondelettes. L’originalité de ce travail repose sur l’usage des ondelettes complexes dont le groupe s’est fait sa ‘marque de commerce’ largement reconnue à l’extérieur (Diego Clonda, Jean-Marc Lina, Bernard Goulard, (2004)). Ce travail exploratoire (K. Christophe, Analyse fractale par ondelettes: application aux mammographies. Rapport de Recherche de DEA, (2003)) a su démontrer une application intéressante dans l’étude thermodynamique du signal en mammographie numérique (modélisation multifractale). Notons que ce contact avec l’INRIA s’est poursuivi avec l’accueil de deux autres étudiants durant l’été 2004. Dans le cadre du travail en analyse fractale, Fahima Nekka a, quant à elle, accueilli deux étudiants de l’INRIA et de l’École Centrale de Nantes (Fr.) pour leur programme de recherche en DEA (co-direction avec Jacques Levy-Vehel et Ina Taralova). Le formalisme multifractal (thermodynamique des signaux) a été appliqué aux images de mammographie numérisées dans le cadre du travail de M.Sc. de Gaël Sitzia (co-direction Bernard Goulard et Jean Marc Lina) qui a mis en place la plateforme logicielle pour effectuer cette analyse. Toujours dans le cadre de l’étude de la mammographie numérisée, on peut souligner le travail d’Isabelle Guimond (M. Ing co-dirigée par Jean-Marc Lina) sur les foyers de micro-calcifi cations en imagerie de biopsie stéréo.

Estimateur du signal EEG en présence d’artefacts oculaires

Une des principales diffi cultés dans l’utilisation de l’électroencéphalographie (EEG) chez les jeunes enfants est la présence, dans le signal, d’artefacts causés par le mouvement oculaire. Ces artefacts sont inévitables et forcent le rejet d’un grand nombre d’acquisi-tions, réduisant ainsi la portée de l’interprétation des expériences EEG en neuro-pédiatrie. Le problème du fi ltrage des signaux, afi n d’en extraire les artefacts, a été exploré dans la représentation temporelle ou fréquentielle. Au cours de ce projet, nous avons mis au point une approche temps-fréquence en utilisant la représentation en ondelettes continue. La performance de cet algorithme est en cours d’évaluation en milieu clinique.

Localisation de sources en MEG/EEG

L’intégration des informations IRMf (Imagerie de Résonance Magnétique Nucléaire fonctionnelle) dans la détection de sources en MEG/EEG (Magnéto-Electro-Encéphalographie) est l’objectif de ce volet de recherche. L’étude d’une méthodologie d’inférence sur le décours temporel des sources d’un modèle dipolaire distribué, capable de prendre en compte des connaissances a priori multimo-dales, est actuellement dans sa phase d’évaluation de performance. Le modèle retenu par Jean Daunizeau (doctorant en co-tutelle entre l’Université de Montréal et Paris11-Orsay, co-direction Habib Benali, Bernard Goulard, Jean-Marc Lina) s’apparente à celui développé dans le cadre du Maximum d’entropie en exprimant la dépendance temporelle à l’échelle de ‘parcelles’ (construites à partir des données) qui contiennent des sources élémentaires qui sont contrastées localement par la méthode d’inférence (Jean Daunizeau, Jérémie Mattout, Bernard Goulard, Jean-Marc Lina, Habib Benali, (2004)). Soulignons que ces méthodes ont fait l’objet d’une évaluation de performance dans un cas clinique bien défi ni (Christophe Grova, Jean Daunizeau, Jean-Marc Lina, Habib Benali, Jean Gotman, (2004)). Cette évaluation terminée, le groupe envisage l’implémentation de la méthodologie dans un environnement de calcul dédié à la multimodalité tel que BrainVisa (développé par Y. Cointepas, CEA, Fr.).

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Graphes et Turbulence

Dans le cadre de la thèse de Doctorat de P. St-Jean (P. St-Jean, Statistique de maxima et Modèles graphiques multi-échelles: Ap-plication à la turbulence, PhD U. de M, (2003)), l’étude des modèles graphiques associés aux modèles des cascades stationnaires a été menée avec succès. Une des contributions importantes consiste dans la statistique d’ordre introduite par P. St-Jean pour décrire le modèle en cascade appliqué à la turbulence. Ce travail permet d’expliquer pour la première fois le modèle de She-Levesque en turbulence pleinement développée (P. St-Jean, An interpretation of the She-Levesque model based on Order Statistics, à paraître dans Eur. Jour. Phys, (2004)).

Études sur les connectivité et plasticité

Étude dirigée par H. Benali de la plasticité cérébrale par imagerie neurofonctionnelle dans son application à la chirurgie des gliomes de bas grade intra-cérébraux avec G. Marrelec, maintenant au centre RMN (Julien Doyon) et en liaison avec J.Daunizau (étudiant au doctorat en cotutelle Benali-Goulard-Lina) qui travaille sur la localisation et la dynamique des sources de l’activité cérébrale par fusion de données IRM fonctionnelles et EEG. Saad Jbabdi (co-tutelle Benali -Joanette ) travaille à la modélisation des connectivités fonctionnelles et anatomiques par imagerie fonctionnelle: application a l’étude des stratégies de la récupération après accident vascu-laire ischémique. S.Jbabdi sera au centre RMN à partir de septembre 2004.

Analyse fractale et Modélisation

F. Nekka et ses étudiants ont développé différentes stratégies de traitement et d’analyse de l’information en fonction du degré de complexité du signal étudié. Elle a considéré l’association de l’analyse fractale et d’outils mathématiques classiques dédiés au traitement de l’information. Cette combinaison a permis de palier certaines lacunes des méthodes classiques et ainsi d’élargir leur champ d’appli-cation pour tenir compte d’une information à haute résolution et de réaliser des progrès en analyse fractale à l’aide de ces méthodes mathématiques classiques très populaires. Dans ce cadre, elle a récemment mis au point une méthode pratique de l’estimation de la dimension de Hausdorff. La précision de cette méthode dépasse largement celle des techniques habituelles (coll. avec A. Arnéodo, Ecole Normale Sup., Lyon, Fr.). Ces méthodes ont été appliquées à l’extraction de l’information et à la classification de structures poreuses, au-delà des paramètres classiques tels que la porosité et la dimension fractale.

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Publications

The CRM publishes monographs, lecture notes, proceedings, software, videos and research reports. It has several collections. The in-house collection Les Publications CRM offers many titles in both English and French. The CRM also has publish-ing agreements with the American Mathematical Society (AMS), Springer-Verlag and International Press. Since 1992, two collections, edited by CRM, have been published and distributed by the AMS. They are the CRM Monograph Series and the CRM Proceedings and Lecture Notes. Springer-Verlag publishes the CRM Series in Mathematical Physics and the CRM Subseries of the Springer Lecture Notes in Statistics. The following list of Recent Titles contains books that have appeared during the year 2002-2003 or that will be published soon. An asterisk preceding an author indicates that this is a monograph from an Aisenstadt Chair holder.

AMS: CRM Monograph Series

• D. Schlomiuk, A. A. Bolibrukh, S. Yakovenko, V. Kaloshin & A. Buium, On Finiteness in Differential Equations and Dio-phantine Geometry, (to appear).

• Olga Kharlampovich & Alexei Myasnikov, Algebraic Geometry for a Free Group, (to appear).

• Montserrat Alsina & Pilar Bayer, Quaternion Orders, Qua-dratic Forms, and Shimura Curves, vol. 22, 2004.

• Prakash Panangaden & Franck van Breugel, Mathematical Techniques for Analyzing Concurrent and Probabilistic Systems, Editors vol. 23, 2004.

AMS: CRM Proceedings & Lecture Notes

• H.E.A Eddy Campbell, David L. Wehlau, Invariant Theory in All Characteristics, vol. 35, 2004.

• Hershy Kisilevsky & Eyal Z. Goren, Number Theory, vol. 36, 2004.

• P. Tempesta, P. Winternitz, J. Harnad, W. Miller Jr., G. Po-gosyan & M. Rodriguez, Superintegrability in Classical and Quantum Systems, vol. 37, 2004.

• Jacques Hurtubise & Eyal Markman, Algebraic Structures and Moduli Spaces: CRM Workshop, July 14-20, 2003, vol. 38, 2004.

Recent Titles

*Publication of the Aisenstadt Chair

Publications

Previous Titles

AMS: CRM Monograph Series

• Andrei Tyurin, Quantization, Classical and Quantum Field Theory and Theta Functions, vol. 21, 2003.

• Joel Feldman, Horst Knörrer & Eugene Trubowitz, Riemann Surfaces of Infinite Genus, vol. 20, 2003.

• *Laurent Lafforgue, Chirurgie des grassmanniennes, vol. 19, 2003.

• *George Lusztig, Hecke Algebras with Unequal Parameters, vol. 18, 2003.

• Michael Barr, Acyclic Models, vol. 17, 2002.

• *Joel Feldman, Horst Knörrer & Eugene Trubowitz, Fermi-onic Functional Integrals and the Renormalization Group, vol.

16, 2002.

• Jose I. Burgos, The Regulators of Beilinson and Borel, vol.15,

2002

• Eyal Z. Goren, Lectures on Hilbert Modular Varieties and Mod-ular Forms, vol. 14, 2002

• Michael Baake & Robert V. Moody (eds.), Directions in Math-ematical Quasicrystals, vol. 13, 2000.

• Masayoshi Miyanishi, Open Algebraic Surfaces, vol. 12, 2001.

• Spencer J. Bloch, Higher Regulators, Algebraic K-Theory, and Zeta Functions of Elliptic Curves, vol. 11, 2000.

• James D. Lewis, A Survey of the Hodge Conjecture, 2e Édition (with an appendix by B. Brent Gordon), vol. 10, 1999.

• Yves Meyer, Wavelets, Vibrations and Scaling, vol. 9, 1997.

• Ioannis Karatzas, Lectures on Mathematics of Finance, vol. 8, 1996.

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• John Milton, Dynamics of Small Neural Populations, vol. 7, 1996.

• Eugene B. Dynkin, An Introduction to Branching Measure-Val-ued Processes, vol. 6, 1994.

• Andrew M. Bruckner, Differentiation of Real Functions, vol. 5, 1994.

• David Ruelle, Dynamical Zeta Functions for Piecewise Monotone Maps of the Interval, vol. 4, 1994.

• V. Kumar Murty, Introduction to Abelian Varieties, vol. 3, 1993.

• Maximilian Ya. Antimirov, Andrei A. Kolyshkin, & Rémi Vail-lancourt, Applied Integral Transforms, vol. 2, 1993.

• Dan V. Voiculescu, Kenneth J. Dykema, & Alexandru Nica, Free Random Variables, vol. 1, 1992.

AMS: CRM Proceedings & Lecture Notes

• André D. Bandrauk, Michel C. Delfour, & Claude Le Bris (édit.), Quantum Control: Mathematical and Numerical Chal-lenges, vol. 33, 2003.

• Vadim B. Kuznetsov (édit.), The Kowalevski Property, vol 32, 2002.

• John Harnad & Alexander R. Its (édit.), Isomonodromic Defor-mations and Applications in Physics, vol. 31, 2002

John McKay & Abdellah Sebbar (eds.), Proceedings on Moonshine and Related Topics, vol. 30, 2001.

• Alan Coley, Decio Levi, Robert Milson, Colin Rogers & Pavel Winternitz (eds.), Bäcklund and Darboux Transformations: The Geometry of Soliton, vol. 29, 2001.

• J. C. Taylor (édit.), Topics in Probability and Lie Groups: Bound-ary Theory, vol. 28, 2001.

• Israel M. Sigal & Catherine Sulem, Nonlinear Dynamics and Re-

normalization Group, vol. 27, 2001.

• John Harnad, Gert Sabidussi & Pavel Winternitz (eds.), Inte-grable Systems: From Classical to Quantum, vol. 26, 2000.

• Decio Levi & Orlando Ragnisco (eds.), SIDE III - Symmetry and Integrability of Difference Equations, vol. 25, 2000.

• B. Brent Gordon, James D. Lewis, Stefan Müller-Stach, Shuji Saito & Noriko Yui (eds.), The Arithmetic and Geometry of Alge-braic Cycles, vol. 24, 2000.

• Pierre Hansen & Odile Marcotte (eds.), Graph Colouring and Applications, vol. 23, 1999.

• Jan Felipe van Diejen & Luc Vinet (eds.), Algebraic Methods and q-Special Functions, vol. 22, 1999.

• Michel Fortin (ed.), Plates and Shells, vol. 21, 1999.

• Katie Coughlin (ed.), Semi-Analytic Methods for the Navier-Stokes Equations, vol. 20, 1999.

• Rajiv Gupta & Kenneth S. Williams (eds.), Number Theory, vol. 19, 1999.

• Serge Dubuc & Gilles Deslauriers (eds.), Spline Functions and the Theory of Wavelets, vol. 18, 1999

• Olga Karlampovich (ed.), Summer School in Group Theory (Banff, 1996), vol. 17, 1998.

• Alain Vincent (ed.), Numerical Methods in Fluid Mechanics (Montréal, 1995), vol. 16, 1998.

• François Lalonde (ed.), Geometry, Topology and Dynamics, (Montréal, 1995), vol. 15, 1998.

• John Harnad & Alex Kasman (eds.), The Bispectral Problem (Montréal, 1997), vol. 14, 1998.

• Michel Delfour (ed.), Boundaries, Interfaces and Transitions (Banff, 1995), vol. 13, 1998.

• Peter G. Greiner, Victor Ivrii, Luis A. Seco & Catherine Sulem (eds.), Partial Differential Equations and their Applications (To-ronto, 1995), vol. 12, 1997.

• Luc Vinet (ed.), Advances in Mathematical Sciences: CRM’s 25 Years (Montréal, 1994), vol. 11, 1997.

• Donald E. Knuth, Stable Marriage and its Relation to Other Com-binatorial Problems. An Introduction to the Mathematical Analysis of Algorithms, vol. 10, 1996.

• Decio Levi, Luc Vinet, & Pavel Winternitz (eds.), Symmetries and Integrability of Difference Equations (Estérel, 1994), vol. 9, 1995.

• Joel S. Feldman, Richard Froese, & Lon M. Rosen (eds.), Math-ematical Quantum Theory II: Schrödinger Operator (Vancouver, 1993), vol. 8, 1995.

• Joel S. Feldman, Richard Froese, & Lon M. Rosen (eds.), Math-ematical Quantum Theory I: Many-Body Theory and Group The-ory (Vancouver, 1993), vol. 7, 1994.

• Guido Mislin (ed.), The Hilton Symposium 1993: Topics in To-pology and Group Theory (Montréal, 1993), vol. 6, 1994.

• Donald A. Dawson (ed.), Measure-valued Processes, Stochastic Partial Differential Equations and Interacting Systems (Montréal, 1992), vol. 5, 1994.

• Hershy Kisilevsky & M. Ram Murty (eds.), Elliptic Curves and Related Topics (Sainte-Adèle, 1992), vol. 4, 1994.

• Andrei L. Smirnov & Rémi Vaillancourt (eds.), Asymptotic Methods in Mechanics, vol. 3, 1993.

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• Philip D. Loewen, Optimal Control via Nonsmooth Analysis, vol. 2, 1993.

• M. Ram Murty (ed.), Theta Functions. From the Classical to the Modern, vol. 1, 1993.

Springer-Verlag: CRM Series in Mathematical Physics

• David Sénéchal, André-Marie Tremblay & Claude Bourbon-nais, Theoretical Methods for Strongly Correlated Electrons, 2003.

• *Roman Jackiw, Lectures on Fluid Dynamics, 2002.

• Yvan Saint-Aubin & Luc Vinet (eds.), Theoretical Physics at the End of the XXth Century. 2001.

• Yvan Saint-Aubin & Luc Vinet (eds.), Algebraic Methods in Phys-ics - A Symposium for the 60th Birthday of Jíri Patera and Pavel Winternitz, 2000.

• Jan Felipe van Diejen & Luc Vinet (eds.), Calogero-Moser-Sutherland Models, 1999.

• Robert Conte (ed.), The Painlevé Property: One Century Later, 1999

• Richard MacKenzie, Manu B. Paranjape & Wojciech J. M. Za-krzewski (eds.), Soliton: Properties, Dynamics, Interactions, Appli-cations, 1999

• Luc Vinet & Gordon Semenoff (eds.), Particles and Fields (Banff, 1994), 1998.

CRM Subseries of the Springer-Verlag Series: Lecture Notes in Statistics

• Marc Moore, Sorana Froda & Christian Léger (eds.), Mathemat-ical Statistics and Applications: Festschrift for Constance van Eeden, vol. 42, 2003.

• S. Ejaz Ahmed & Nancy Reid (eds.), Empirical Bayes and Likeli-hood Inference, 2001.

• Marc Moore (ed.), Spatial Statistics, 2001.

Les Publications CRM

• Luc Lapointe, Ge Mo-Lin, Yvan Saint-Aubin & Luc Vinet, Proceedings of the Canada-China Meeting on Theoretical Physics, 2003.

• Armel Mercier, Fonctions de plusieurs variables: Différentiation, 2002.

• (Nadia El-Mabrouk, Thomas Lengauer & David Sankoff (eds.), Currents in Computational Molecular Biology 2001..

• James G. Huard & Kenneth S. Williams (eds.), The Collected

Papers of Sarvadaman Chowla, I, II, III, 2000.

• Michael Barr & Charles Wells, Category Theory for Computing Science, 1999

• Maximilian Ya. Antimirov, Andrei A. Kolyshkin & Rémi Vail-lancourt, Mathematical Models for Eddy Current Testing, 1998.

• Xavier Fernique, Fonctions aléatoires gaussiennes, vecteurs aléa-toires gaussiens, Montréal, 1997.

• Faqir Khanna & Luc Vinet (eds.), Field Theory, Integrable Sys-tems and Symmetries, Montréal, 1997.

• Paul Koosis, Leçons sur le théorème de Beurling at Malliavin, 1996.

• David W. Rand, Concorder Version Three: Concordance Software for the Macintosh, Montréal, 1996 (software and user guide).

• Decio Levi, Curtis R. Menyuk, & Pavel Winternitz, Self-Simi-larity in Stimulated Raman Scattering (Montréal, 1993), Mon-tréal, 1994.

• Jacques Gauvin, Theory of Nonconvex Programming, Montréal, 1994.

• Rémi Vaillancourt, Compléments de mathématiques pour ingé-nieurs, Montréal, 1993.

• Robert P. Langlands & Dinakar Ramakrishnan (eds.), The Zeta Functions of Picard Modular Surfaces (Montréal, 1988), Mon-tréal, 1992.

• Florin N. Diacu, Singularities of the N-Body Problem, Montréal, 1992.

• Jacques Gauvin, Théorie de la programmation mathématique non convexe, Montréal, 1992.

• Pierre Ferland, Claude Tricot, & Axel van de Walle, Analyse fractale: Application Windows™ 3.x d’initiation aux ensembles fractals, Montréal, 1992 (software and user guide).

• Stéphane Baldo, Introduction à la topologie des ensembles fractals, 1991.

• Robert Bédard, Groupes linéaires algébriques, Montréal, 1991.

• Rudolf Beran & Gilles R. Ducharme, Asymptotic Theory for Boot-strap Methods in Statistics, Montréal, 1991.

• James D. Lewis, A Survey of the Hodge Conjecture, Montréal, 1991.

• David W. Rand & Tatiana Patera, Concorder: Concordance Software for the Macintosh, Montréal, 1991 (software and user guide).

• David W. Rand & Tatiana Patera, Le Concordeur: un logiciel de concordances pour le Macintosh, Montréal, 1991 (software and user guide).

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• Véronique Hussin (ed.), Lie Theory, Differential Equations and Representation Theory (Montréal, 1989), Montréal, 1990.

• John Harnad & Jerrold E. Marsden (eds.), Hamiltonian Systems, Transformation Groups and Spectral Transform Methods (Mon-tréal, 1989), Montréal, 1990.

• M. Ram Murty (ed.) Automorphic Forms and Analytic Number Theory (Montréal, 1989), Montréal, 1990.

• Wendy G. McKay, Jirí Patera & David W. Rand, Tables of Rep-resentations of Simple Lie Algebras. I. Exceptional Simple Lie Alge-bras, Montréal, 1990.

• Anthony W. Knapp, Representations of Real Reductive Groups, Montréal, 1990.

• Wendy G. McKay, Jirí Patera & David W. Rand, SimpLie User’s Manual–Macintosh Software for Representations of Simple Lie Al-gebras, Montréal, 1990 (software and user guide).

• Francis H. Clarke, Optimization and Nonsmooth Analysis, Mon-tréal, 1989.

• Hedy Attouch, Jean-Pierre Aubin, Francis Clarke & Ivar Eke-land (eds.), Analyse non linéaire (Perpignan, 1987), Paris & Montréal, Gauthiers-Villars, 1989.

• Samuel Zaidman, Une introduction à la théorie des équations aux dérivées partielles, Montréal, 1989.

• Lucien Le Cam, Notes on Asymptotic Methods in Statistical Deci-sion Theory, Montréal, 1974.

AMS/International Press

• Duong H. Phong, Luc Vinet & Shing-Tung Yau (eds.), Mirror Manifolds and Geometry, AMS/IP Studies in Advanced Math-ematics, American Mathematical Society, Providence, RI, In-ternational Press, Cambridge, MA, & CRM, Montréal, 1998 (vol.10).

Aisenstadt Chair Collection

• Yuri I. Manin, Quantum Groups and Noncommutative Geometry, Les Publications CRM, 1988.

• Laurent Schwartz, Semimartingales and Their Stochastic Calculus on Manifolds, Presses de l’Université de Montréal, 1984.

• Yuval Ne’eman, Symétries, jauges et variétés de groupe, Presses de l’Université de Montréal, 1979.

• R. Tyrrell Rockafellar, La théorie des sous-gradients et ses applica-tions à l’optimisation, fonctions convexes et non convexes, Presses de l’Université de Montréal, 1979.

• Jacques-Louis Lions, Sur quelques questions d’analyse, de méca-nique et de contrôle optimal, Presses de l’Université de Montréal, 1976.

• Donald E. Knuth, Mariage stables et leurs relations avec d’autres problèmes combinatoires, Presses de l’Université de Montréal, 1976.

• Robert Hermann, Physical Aspects of Lie Group Theory, Presses de l’Université de Montréal, 1974.

• Mark Kac, Quelques problèmes mathématiques en physique statis-tique, Presses de l’Université de Montréal, 1974.

• Sybreen de Groot, La transformation de Weyl et la fonction de Wigner: une forme alternative de la mécanique quantique, Presses de l’Université de Montréal, 1974.

Miscellaneous

• Pierre Ferland, Claude Tricot, & Axel van de Walle, Fractal analysis user’s guide. Introduction to fractal sets using Windows™ 3.x., American Mathematical Society, Providence, RI & Centre de recherches mathématiques, Montréal, 1994.

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Publications

Preprints and Research ReportsAguiar, M., Bergeron, N., Sottile, F., Combinatorial Hopf al-gebras and generalized Dehn-Sommerville relations, ArXiv:math.CO/0310016, October 2003.

Ali, S. T., Englis, M., Quantization methods: a guide for physicists and analysts, ArXiv:math-ph/0405065, May 2004.

Ali, S. T., Englis, M., Gazeau, J.-P., Vector coherent states from Plancherel’s theorem and Clifford algebras, arXiv:math-ph/0311042, November 2003.

Ali, S. T., Hohouéto, A. L., Thirulogasanthar, K., Coherent states lattices for a class of semi-direct product groups, Concordia Uni-versity.

Andreatta, F., Goren, E. Z., Hilbert modular forms: mod p and p-adic aspects, Amer. Math. Soc., arXiv:math.NT/0308040, Au-gust 2003.

Angers, J.-F., MacGibbon, B., Bayesian functional estimation of the hazard rate for randomly right censored data using Fourier series methods, GERAD, G-2004-36, April 2004.

Angers, J.-F., Merleau, J., Perreault, L., Registration of hydro-graphs and Bayesian estimation of a mean hydrograph, Centre de recherches mathématiques, CRM-3023, May 2004.

Apostolov, V., Calderbank, D. J., Gauduchon, P., Tonnesen-Friedman, C. W., Hamiltonian 2-forms in Kähler geometry. II. Global classification, arXiv:math.DG/0401320, January 2004.

Apostolov, V., Draghici, T., Moroianu, A., The odd-dimensional Goldberg conjecture, arXiv:math.DG/0308241, August 2003.

Arminjon, P., Touma, R., A central, diamond-staggered dual cell, finite volume method for ideal magnetohydrodynamics, Centre de recherches mathématiques, CRM-2935, October 2003.

Ashino, R., Desjardins, S. J., Heil, C., Nagase, M., Vaillancourt, R., Pseudodifferential operators, microlocal analysis and image restoration, Centre de recherches mathématiques, CRM-2985, December 2003.

Ashino, R., Desjardins, S. J., Heil, C., Nagase, M., Vaillancourt, R., Image restoration through microlocal analysis with smooth tight wavelet frames, Centre de recherches mathématiques, CRM-2926, June 2003.

Ashino, R., Desjardins, S. J., Kolyshkin, A. A., Vaillancourt, R., Noise smoothing in the Fourier domain by a multi-directional dif-fusion», Centre de recherches mathématiques, CRM-2934, Sep-tember 2003.

Ashino, R., Morimoto, A., Nagase, M., Vaillancourt, R., Com-paring multiresolution SVD with other methods for image compres-sion, Centre de recherches mathématiques, CRM-2987, March 2004.

Ashino, R., Morimoto, A., Nagase, M., Vaillancourt, R., Im-age compression with multiresolution singular value decomposition and other methods, Centre de recherches mathématiques, CRM-2939, January 2004.

Ashino, R., Nagase, M., Vaillancourt, R., Pseudodifferential op-erators in lp(rn) spaces», Centre de recherches mathématiques, CRM-2967, December 2003.

Attal, S., Pautrat, Y., From repeated to continuous quantum inter-actions, arXiv:math-ph/0311002, November 2003.

Ban, D., Zhang, Y., Arthur R-groups, classical R-groups and Au-bert involution, Centre de recherches mathématiques, CRM-2922a, June 2003.

Baribeau, L., Roy, M., Holomorphic iterated function systems, submitted.

Bertola, M., Second and third order observables of the two-matrix model, Centre de recherches mathématiques, CRM-2931, Sep-tember 2003.

Bertola, M., Free energy of the two-matrix model/dToda tau-func-tion, Centre de recherches mathématiques, CRM-2921, June 2003.

Bertola, M., Eynard, B., The PDEs of biorthogonal polynomials arising in the two-matrix model, CEA Saclay, SPhT-T03/139, November 2003.

Bertola, M., Eynard, B., Harnad, J., Generalized matrix models with rational potentials and isomonodromic tau functions, Centre de recherches mathématiques, CRM-3053, 2004.

Bertola, M., Eynard, B., Harnad, J., Semiclassical orthogonal poly-nomials, matrix models and isomonodromic tau functions, Centre de recherches mathématiques, CRM-3169, January 2004.

Bouhaddioui, C., Roy, R., On the distribution of the residual cross-correlations between two uncorrelated infinite order vector autoregressive series, Centre de recherches mathématiques, CRM-2924, June 2003.

Boyer, S., Culler, M., Shalen, P., Zhang, X., Characteristic sub-surfaces, character varieties and Dehn filling II, Université du Québec à Montréal, 2004.

Charron, M., Houtekamer, P., Bartello, P., Assimilating synthetic radar data at the mesoscale witn an ensemble Kalman filter: a per-fect model experiment, Monthly Weather Review, submitted.

Chaubey, Y., De Souza, C., Nebebe, F., Bayesian inference for small area estimation under the inverse Gaussian model via Gibbs Sampling, Department of Mathematics & Statistics, Concordia University, 4/03, 2003.

Colin, F., Frigon, M., Systems of coupled Poisson equations with critical growth in unbounded domains, Centre de recherches mathématiques, CRM-2933, June 2003.

Cornea, O., Barraud, J.-F., Lagrangian intersections and the Serre spectral sequence, arXiv:math.DG/0401094, January 2004.

D’Amico, A., Van Vliet, C. M., Excess noise measurements of com-posite polymer resistive sensors, Sensors and Actuators, submitted.

Dorodnitsyn, V., Kozlov, R., Winternitz, P., Continuous symme-tries of Lagrangians and exact solutions of discrete equations, Cen-

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tre de recherches mathématiques, CRM-2990, July 2003.

Dryanov, D., Fournier, R., On Ruscheweyh’s improvement of Ber-nstein’s inequality, Centre de recherches mathématiques, CRM-3123, May 2004.

Dryanov, D., Fournier, R., Ruscheweyh, S., Some extensions of the Markov inequality for polynomials, Centre de recherches mathématiques, CRM-3122, May 2004.

Duchesne, P., On the asymptotic distribution of residual autoco-variances in VARX models with applications, Test, submitted.

Duchesne, P., On testing for serial correlation with a wavelet-based spectral density estimator in multivariate time series, Econometric Theory, submitted.

Duchesne, P., Hong, Y., Wavelet-based detection for duration clustering and adequacy of autoregressive conditional duration models, J. Econometrics, submitted.

Duchesne, P., Pacurar, M., On testing for duration clustering and diagnostic checking of models for irregularly spaced transaction data, Econom. J., submitted.

El-Fallah, O., Kellay, K., Ransford, T., Cyclic vectors for the Dirichlet space and Bergman-Smirnov exceptional sets, submitted.

Fearnley, J., Kisilevsky, H., Vanishing and non-vanishing Dirich-let twists of L-functions of elliptic curves, Concordia University, 2004.

Fearnley, J., Kisilevsky, H., Vanishing and non-vanishing Dirich-let twists of L-functions, Concordia University, 2004.

Finster, F., Kamran, N., Smoller, J., Yau, S.-T., An integral spec-tral representation of the propagator for the wave equation in the Kerr geometry, arXiv:gr-qc/0310024, October 2003.

Fortin, J.-F., Jacob, P., Mathieu, P., Jagged partitions, arXiv:math.CO/0310079, October 2003.

Fortin, J.-F., Jacob, P., Mathieu, P., Generating function for K-restricted jagged partitions, arXiv:math-ph/0305055, May 2003.

Fournier, R., On a variation of the Bernstein inequality for poly-nomials, Centre de recherches mathématiques, CRM-3124, May 2004.

Fournier, R., Dryanov, D., Bernstein and Markov type inequali-ties, Centre de recherches mathématiques, CRM-2929, August 2003.

Francq, C., Roy, R., Zakoian, J.-M., Goodness-of-fit tests for ARMA models with uncorrelated errors Centre de recherches mathématiques, CRM-2925, July 2003.

Frank, G., Hua, X., Vaillancourt, R., Uniqueness of meromorphic functions, Centre de recherches mathématiques, CRM-3017, April 2004.

Frank, G., Hua, X., Vaillancourt, R., Meromorphic functions sharing the same zeros and poles, Centre de recherches mathéma-tiques, CRM-3018, April 2004.

Franklin, C. N., Vaillancourt, P. A., Yau, M.-K., Bartello, P., Collision rates of cloud droplets in turbulent flow, J. Atmospheric

Sci, submitted.

Gomez-Ullate, D., Kamran, N., Milson, R., Quasi-exact solv-ability and the direct approach to invariant subspaces, ArXiv:nlin.SI/0401030, January 2004.

Goren, E. Z., Lauter, K., Class invariants for quartic CM fields, arXiv:math.NT/0404378, April 2004.

Goyou-Beauchamp, D., Leroux, P., Enumeration of symmetry classes of convex polyominoes on the honeycomb lattice, arXiv:math.CO/0403168, March 2004.

Granville, A., Soundararajan, K., The number of unsieved integers up to x, arXiv:math.NT/0308009, August 2003.

Griffiths, R., Lessard, S., Ewens’ sampling formula and related formulae: combinatorial proofs, extensions to variable population size and applications to ages of alleles, Theoret. Population Biol. submitted.

Hajji, A., Melkonian, S., Vaillancourt, R., Two-dimensional wavelet bases for partial differential operators and applications, Centre de recherches mathématiques, CRM-2986, December 2003.

Harnad, J., Janossy densities, multimatrix spacing distributions and Fredholm resolvents, arXiv:math-ph/0403007, March 2004.

Harnad, J., Loutsenko, I., Yermolayeva, O., Constrained reduc-tions of 2D dispersionless Toda hierarchy, Hamiltonian structure and interface dynamics, arXiv:math-ph/0312058, December 2003.

Hsu, T., Wise, D. T., Groups with infinitely many fixed subgroups, McGill University, August 2003.

Hurtubise, J., Jeffrey, L., Sjamaar, R., Group-valued implosion and parabolic structures, arXiv:math.SG/0402464, February 2004.

Jaksic, V., Last, Y., Simplicity of singular spectrum in Anderson type Hamiltonians, submitted.

Kalnins, E. G., Thomova, Z., Winternitz, P., Subgroup type co-ordinates in four-dimensional flat spaces, J. Math. Phys., submit-ted.

Kalnins, E. G., Thomova, Z., Winternitz, P., Subgroup type coordinates in four-dimensional flat spaces, Centre de recherches mathématiques, CRM-3012, May 2004.

Khare, C., Larsen, M., Ramakrishna, R., Constructing semisim-ple p-adic Galois representations with prescribed properties, arXiv:math.NT/0309283, September 2003.

Khare, C., Larsen, M., Ramakrishna, R., Transcendental l-adic Galois representations, arXiv:math.NT/0404254, April 2004.

Kokotov, A., Korotkin, D., Normalized Ricci flow on Riemann surfaces and determinant of Laplacian, arXiv:math.SP/0405010, May 2004.

Korotkin, D., Solution of matrix Riemann-Hilbert problem with quasi-permutation monodromy matrices, arXiv:math-ph/0306061, June 2003.

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Labelle, G., Lamathe, C., Leroux, P., Labelled and unlabelled enumeration of k-gonal 2-trees, arXiv:math.CO/0312424, De-cember 2003.

Labelle, J., The outer-automorphisms of the symmetric group S6 and 1-factorisations of K6, J. Combin. Theory Ser. A, submit-ted.

Lalonde, F., A field theory for symplectic fibrations over surfaces, arXiv:math.SG/0309335, September 2003.

Leroux, P., Enumerative problems inspired by Mayers’ theory of cluster integrals, Centre de recherches mathématiques, arXiv:math.CO/0401001, January 2004.

Lesage, F., Lina, J.-M., Minimax entropy principle for brain activ-ity detection from magnetoencephalography, NeuroImage, submit-ted.

Levi, D., Tempesta, P., Winternitz, P., Lorentz and Galilei in-variance on lattices, Centre de recherches mathématiques, CRM-2974, October 2003.

Machida, H., Rosenberg, I. G., Monoids whose centralizer is the least clone, Hitotsubashi University, October 2003.

McCammond, J. P., Wise, D. T., Locally quasiconvex small-can-cellation groups, McGill University, September 2003.

McCammond, J. P., Wise, D. T., Windmills and extreme 2-cells, McGill University, August 2003.

Morimoto, A., Ashino, R., Vaillancourt, R., Pre-processing design for multiwavelet filters using neural networks, Centre de recher-ches mathématiques, CRM-2980, March 2004.

Nachtergaele, B., Spitzer, W., Starr, S. L., Ferromagnetic ordering of energy levels, J. Statist. Phys., submitted.

Penskoi, A. V., Canonically conjugate variables for the periodic Camassa-Holm equation, arXiv:math-ph/0311036, November 2003.

Penskoi, A. V., Winternitz, P., Discrete matrix Riccati equations with superposition formulas, Centre de recherches mathéma-tiques, CRM-2976, May 2003.

Petridis, Y. N., Risager, M. S., The distribution of values of the Poincaré pairing for hyperbolic Riemann surfaces, arXiv:math.NT/0311010, November 2003.

Petridis, Y. N., Risager, M. S., Modular symbols have a normal distribution, arXiv:math.NT/0308120, August 2003.

Ransford, T., Valley, M., Subharmonicity in von Neumann alge-bras, submitted.

Ratnarajah, T., Vaillancourt, R., Quadratic forms on complex random matrices and multi-antenna channel capacity, Centre de recherches mathématiques, CRM-2979, March 2004.

Ratnarajah, T., Vaillancourt, R., Correlated MIMO channel ca-pacity, Centre de recherches mathématiques, CRM-2937, No-vember 2003.

Ratnarajah, T., Vaillancourt, R., Alvo, M., Complex random matrices and applications, Centre de recherches mathématiques,

CRM-2938, January 2004.

Ratnarajah, T., Vaillancourt, R., Alvo, M., Complex random ma-trices and Rayleigh channel capacity, Centre de recherches mathé-matiques, CRM-2930, June 2003.

Ratnarajah, T., Vaillancourt, R., Alvo, M., Jacobians and hyper-geometric functions in complex multivariate analysis, Centre de recherches mathématiques, CRM-2927, July 2003.

Ratnarajah, T., Vaillancourt, R., Alvo, M., Eigenvalues and con-dition numbers of complex random matrices, Centre de recherches mathématiques, CRM-3022, April 2004.

Rodríguez, M. A., Winternitz, P., Lie symmetries and exact solu-tions of first order difference schemes, Centre de recherches mathé-matiques, CRM-2988, February 2004.

Rousseau, C., Divergent series: past, present, future..., Centre de recherches mathématiques, CRM-3016, April 2004.

Rousseau, C., Christopher, C., Normalizable, integrable and linearizable saddle points in the Lotka-Volterra system, Centre de recherches mathématiques, CRM-2921a, April 2003.

Roy, R., Bouhaddioui, C., A generalized portmanteau test for in-dependence of two infinite order vector autoregressive series, Centre de recherches mathématiques, CRM-2936, December 2003.

Sageev, M., Wise, D. T., The Tits alternative for CAT(0) cubical complexes, arXiv:math.GR/0405022, May 2004.

Schlomiuk, D., Vulpe, N., Planar quadratic differential systems with invariant straight lines of the total multiplicity 4, Centre de recherches mathématiques, CRM-2940, March 2004.

Tavoularis, S., Sahrapour, A., Ahmed, N. U., Madrane, A., Vail-lancourt, R., Towards optimal control of blood flow in artificial hearts, Centre de recherches mathématiques, CRM-2928, Au-gust 2003.

Winternitz, P., Symmetries of discrete systems, Centre de recher-ches mathématiques, CRM-2989, September 2003.

Winternitz, P., Symmetries of discrete systems, Centre de recher-ches mathématiques, CRM-2932, September 2003.

Wise, D., Sectional curvature, compact cores, and local-quasicon-vexity, McGill University, November 2003.

Wise, D., Cubalating small-cancellation groups, McGill Univer-sity, November 2003.

Wise, D., Approximating flats by periodic flats in CAT(0) square complexes, McGill University, 2003.

Wise, D., Positive one-relator groups are coherent, McGill Univer-sity, September 2003.

Wise, D., The coherence of one-relator groups with torsion, and the Hanna Neumann conjecture, McGill University, February 2004, 8 p.

Wise, D., Complete square complexes, McGill University, No-vember 2003.

Wise, D., Nonpositive sectional curvature for (p, q, r)-complexes, McGill University, January 2004.

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Scientific PersonnelLong-term visitorsEach year the CRM hosts a large number of visitors. The majority come to the centre to participate in scientific activities organized or co-organized by the CRM. In the year 2003-2004, 499 such participants registered for workshops of the the-matic program, 796 in activities of the general program and 478 in those of the industrial and multidisciplinary program. In addition, the CRM helped fund several other scientific events. The following list includes only visitors who were in residence for at least four weeks:

Ashot Akhperjanian

Yerevan Physics Institute

Jamil Aouidi

Faculté des Sciences de Bizerte

Dario Bambusi

Università degli studi di Milano

Habib Benali

CHU Pitié Salpêtrière

Yves Bourgault

University of Ottawa

Ligia-Lucia Brinzanescu

Institute of Mathematics “Simon Stoilow”

Vasile Brinzanescu

Institute of Mathematics “Simon Stoilow”

Philippe Caldero

Institut Gérard Desargues

Gianni Cassinelli

Universita di Genova

Colin Christopher

University of Plymouth

Walter Craig

McMaster University

Stephan De Bièvre

Univ. des Sciences et Technologies de Lille

Zindine Djadli

Université de Cergy-Pontoise

Vladimir Dorodnitsyn

Keldysh Institute of Applied Mathematics

Victor Enolskii

National Academy of Sciences of Ukraine

Bertrand Eynard

CEA Centre d’études de Saclay

John Friedlander

University of Toronto

André Garon

École Polytechnique de Montréal

Nassif Ghoussoub

University of British Columbia

Piotr P. Goldstein

The Andrzej Soltan Institute for Nuclear Studies

Jaroslav Hlinka

Czech Technical Institute

Yakar Kannai

Weiszmann Institute of Sciences

Andrei Kapaev

Russian Academy of Sciences

Jamila Karrakchou

École Mohammadia d’ingénieurs

Iryna Kashuba

Universidade de Sao Paulo

Anatoliy Klimyk

Bogolyubov Institute for Theoretical Physics

Margarita Kraus

Universität Regensburg

Decio Levi

Universita’ di Roma Tre

Michael Levitin

Heriot-Watt University

Dan Mangoubi

Technion Israel Institute of Technology

Luigi Martina

Universita di Lecce

Vladimir Matveev

Université de Bourgogne

V. Mikhailov

University of Leeds

Werner Müller

Universität Bonn

Yousuke Ohyama

Osaka University

Shoji Okumura

Osaka University

Abdellatif Ouansafi

Université de Montréal

Yiannis N. Petridis

City University of New York Lehman College

Michael P. Polis

Oakland University

Roman Popovych

National Academy of Sciences of Ukraine

Emma Previato

Boston University

Alexander Pushnitski

Loughborough University

Peter Russell

McGill University

Vardan Sahakyan

Yerevan Physics Institute

Zora Thomova

SUNY-Institute of Technology

Hideaki Ujino

Gunmaa College of Technology

Nicolae Vulpe

Academy of Sciences of Moldova

Clarence Eugene Wayne

Boston University

Eduard Zehnder

ETH-Zentrum

Peter Zeiner

Technische Universitaet Wien

Eduardo Santillan Zeron

Cinvestav-IPN (Institut Polytechnique National)

Yuanli Zhang


59

Annual R

eport CR

M 2003-2004

Scientific P

ersonnel

Alain Arnéodo

C.N.R.S.

Joan Carles Artes

Universitat autonoma de Barcelona

Davide Batic


Habib Benali

CHU Pitié Salpêtrière

Edward Bierstone


Pieter Blue

Rutgers University

Alexander Bobenko

Technische Universitat Berlin

Jochen Brüning

Humboldt-Universität zu Berlin

John P. D’Angelo

University of Illinois, Urbana-Champaign

Lawrence Ein

University of Illinois at Chicago

Miroslav Englis

Academy of Sciences of the Czech Republic

Felix Finster


Roberto Floreanini

INFN

Peter Forgacs

Université de Tours

Akito Futaki

Tokyo Institute of Technology

Allan Greenleaf

University of Rochester

Jotun Hein

University of Oxford

Willy Hereman

Colorado School of Mines

Eugénie Hunsicker

Lawrence University

Andreas Im Hof

Universität Basel

John Kececioglu

University of Arizona

Jeroen Lamb

Imperial College

Robert Lazarsfeld

University of Michigan

Jeong-Yup Lee


Frank Lemire

University of Windsor

Ben Lichtin

University of Rochester

John Loftin

Columbia University

Zhiqin Lu

UC Irvine

Toshiki Mabuchi

Osaka University

Rafe Mazzeo

Stanford University

Jeffery McNeal

The Ohio State University

Eckhard Meinrenken


Richard Melrose

MIT

Alexander Mikhailov

University of Leeds

Pierre Milman


Mircea Mustata

Clay Mathematics Institute

Thomas Nevins

University of Michigan

Andreea C. Nicoara

Harvard University

Takeo Ohsawa

Nagoya University

Zbigniew Oziewicz

Universidad Nacional Autonoma de Mexico

Short-term visitors

Wieslaw Pawlucki

Jagiellonian University

Duong H. Phong

Columbia University

Michael P. Polis

Oakland University

Mathieu Raffinot

Université d’Evry

Leslie D. Saper

Duke University

Harald Schmid


Misha B. Sheftel

North Western State Technical University

Alexandre Shnirelman

University of Hull

Jacob Sturm

Rutgers University

Marc Thiriet

INRIA Rocquencourt, Projet M3N

Zora Thomova

SUNY-Institute of Technology

Leopold Vrana

Czech Technical University in Prague

Stephen Wainger

University of Wisconsin-Madison

Gregor Weingart

Universität Bonn

Ben Weinkove

Columbia University

Norman Wildberger

University of New South Wales

Jaroslaw Wlodarczyk

Purdue University

Jared Wunsch

Northwestern University

Chan Woo Yang

Johns Hopkins University

Roman Zelazny

Institute of Plasma Physics & Laser Microfusion

Visitors who were in residence for less than four weeks:

60

Ann

ual R

epor

t CR

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003-

2004

Alain Bourget

McMaster University

Peter S. Campbell


Raquel Casesnoves


Stéphane Dellacherie

Université de Paris 7

Mostafa Gabbouhy

Université Ibn Tofaïl (Maroc)

David T. Gay

University of California Berkeley

David Gómez-Ullate

Universidad complutense de Madrid

Alexander Ivrii

Stanford University

Sergei Krutelevich

Yale University

Marcelo Lanzilotta Mernies

Université de la République, (Uruguay)

Vincent Lemaire


Jun Li


Peter McNamara

Massachusetts Institute of Technology

Marco Merkli


Ramin Mohammadalikhani


Brian E. Moore

University of Surrey

Ambrus Pal

Columbia University

Yan Pautrat

Institut Fourier

Alexei V. Penskoi


Bélà Gabor Pusztai

University of Szeged

Mario Roy

University of Göttingen

Anupam Saikia

University of Cambridge

Postdoctoral FellowsEach year the CRM plays host to a great number of postdoctoral fellows. The sources for their funding include the NSERC and FQRNT postdoctoral programs, the NATO international program administered by NSERC, the CRM (usually with the ISM), the CRM’s research laboratories, and individual research grants from CRM members. The list below includes post-doctoral fellows in residence at the CRM and those funded or co-funded by the CRM. Some of the fellows were in residence at the CRM for only part of the year – the affiliation is that where their doctoral degree was obtained.

Mohamed Noureddine Senhadji

Université d’Oran

Libor Snobl

Czech Technical Institute

Shannon Lee Starr

University of California

Phi Long Nguyen Thanh

Columbia University

Stephan Tillmann

University of Melbourne

Michèle Suzanne Titcombe

University of British Columbia

Sébastien Tremblay


José Manuel Urquiza

Université de Paris 6

Dimiter Vassilev

Purdue University

Alexander Zhalij

Inst. of Mathematics of the National Academy of

Sciences, Ukraine

61

Annual R

eport CR

M 2003-2004

Scientific P

ersonnel

Syed Twareque Ali Concordia University

Jean-François Angers Université de Montréal

Vestislav Apostolov UQAM

Paul Arminjon Université de Montréal

André D. Bandrauk Université de Sherbrooke

Line Baribeau Université Laval

Peter Bartello McGill University

Liliane Beaulieu Cégep du Vieux Montréal

Robert BédardUQAM

Jacques Bélair Université de Montréal

Habib Benali CHU Pitié-Salpêtrière

Yoshua Bengio Université de Montréal

Anne Bergeron UQAM

François BergeronUQAM

Nantel BergeronYork University

Marco Bertola Concordia University

Yves Bourgault University of Ottawa

Anne Bourlioux Université de Montréal

Steven BoyerUQAM

Gilles BrassardUniversité de Montréal

Abraham Broer Université de Montréal

Robert C. Brunet Université de Montréal

David BryantMcGill University

Yogendra P. Chaubey Concordia University

Francis H. Clarke Claude Bernard Lyon 1

Olivier Collin UQAM

Robert Conte CEA Saclay

Octavian Cornea Université de Montréal

In contrast with most other mathematics institutes around the world, the CRM can count on the solid foundation of regular, associate and invited members. Regular members are all professors at partner institutions: Université de Montréal, Concor-dia University, McGill University, UQAM, Université Laval, Université de Sherbrooke and the University of Ottawa. Other members are researchers attached to the CRM in 2003-2004 as part of exchange agreements with neighbouring universities and industry or are long-term visitors from Canadian and foreign institutions. The presence at the CRM of such an active group of researchers has brought many benefits to the centre. In particular, the CRM’s national program is greatly facilitated by having on hand a large reserve of willing organizers, who have even contributed financially to the organization of activi-ties. The largest partnership is with the Université de Montréal, which gives the equivalent of five fulltime teaching positions in release time to the CRM. Release agreements with the other Montréal area universities provide for the equivalent of two more full-time positions. Facilities are also provided to researchers attached to junior colleges. Several members are attached to the CRM through industrial agreements.

Claude CrépeauMcGill University

Miklos CsürösUniversité de Montréal

Chris CumminsConcordia University

Galia DafniConcordia University

Henri DarmonMcGill University

Chantal DavidConcordia University

Michel C. DelfourUniversité de Montréal

Eusebius J. DoedelConcordia University

Louis G. Doray Université de Montréal

Rachida DssouliConcordia University

Pierre Duchesne Université de Montréal

Stéphane Durand Collège Edouard-Montpetit

Nadia El-MabroukUniversité de Montréal

Richard Fournier Dawson College

CRM Members in 2003-2004

Here is the list of regulars, associed and invited members of the CRM:

62

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ual R

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t CR

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2004

Marlène Frigon Université de Montréal

Martin J. Gander McGill University

José Garrido Concordia University

Paul M. GauthierUniversité de Montréal

Eyal Z. Goren McGill University

Bernard Goulard Université de Montréal

Andrew GranvilleUniversité de Montréal

Alfred Michel Grundland UQTR

Richard L. Hall Concordia University

Michael HallettMcGill University

John Harnad Concordia University

Antony R. HumphriesMcGill University

Jacques HurtubiseMcGill University

Véronique Hussin Université de Montréal

Adrian IovitaConcordia University

Dmitry JakobsonUniversité de Montréal

Vojkan Jaksic McGill University

Niky Kamran McGill Universityl

Olga KharlampovichMcGill Universityl

Hershy KisilevskyMcGill University

Paul Koosis McGill University

Dmitry Korotkin Concordia University

Gilbert Labelle UQAM

Jacques Labelle UQAM

François Lalonde Université de Montréal

Robert P. Langlands Institute for Advanced Study

Christian Léger Université de Montréal

Dietmar Leisen Johannes Gutenberg-Universität Mainz

Pierre LerouxUQAM

Frédéric Lesage ART Advanced Research Technologies Inc.

Sabin Lessard Université de Montréal

Jean LeTourneux Université de Montréal

Claude Levesque Université Laval

Decio Levi Universita’ di Roma Tre

Jun Li Université de Montréal

Jean-Marc Lina École de Technologie Supérieure

Brenda MacGibbonUQAM

François MajorUniversité de Montréal

Vladimir Makarenkov UQAM

Michael Makkai McGill University

Patrice Marcotte Université de Montréal

Javad Mashreghi Université Laval

Sherwin A. Maslowe McGill University

Pierre Mathieu Université Laval

John McKay Concordia University

Pierre McKenzie Université de Montréal

Alexei G. Miasnikov McGill University

Fahima Nekka Université de Montréal

Nilima NigamMcGill University

Jiri Patera Université de Montréal

François PerronUniversité de Montréal

Yiannis N. Petridis City Univ. of New York Lehman College

Iosif Polterovich Université de Montréal

Ravi Ramakrishna Cornell University

Thomas J. Ransford Université Laval

Christophe ReutenauerUQAM

Ivo G. Rosenberg Université de Montréal

CRM members in 2003-2004 - continued

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Annual R

eport CR

M 2003-2004

Scientific P

ersonnel

Christiane Rousseau Université de Montréal

Damien Roy University of Ottawa

Roch Roy Université de Montréal

Peter Russell McGill University

Gert Sabidussi Université de Montréal

Yvan Saint-Aubin Université de Montréal

David Sankoff University of Ottawa

Dana Schlomiuk Université de Montréal

E. J. P. Georg Schmidt McGill University

Abdellah Sebbar University of Ottawa

Elisa Shahbazian Lockheed Martin Canada

Ron J. Stern Concordia University

Francisco Thaine Concordia University

John A. Toth McGill University

Pierre Valin Defence R & D Canada - Valcartier

Carolyne M. Van Vliet Univerity of Miami

Luc Vinet McGill University

Pavel WinternitzUniversité de Montréal

Daniel T. Wise McGill University

Keith J. Worsley McGill University

Jean-Paul Zolésio INRIA

CRM members in 2003-2004 - continued

64

Ann

ual R

epor

t CR

M 2

003-

2004

Yoshua BengioUniversité de Montréal

François BergeronUQAM

Alain CailléVice-recteur à la recherche,Université de Montréal

Antony Humphries*

McGill University

Joseph HubertDoyen, Faculté des arts et des sciences, Université de Montréal

Hershy KisilevskyConcordia University

Jean LeTourneux*Université de Montréal

Christian LégerUniversité de Montréal

Bureau de directionThe Bureau consists of members from the Université de Montréal (eight to eleven members) and from the outside (two to five members). The rector of the Université de Montréal and the Dean of its Arts and Sciences faculty are represented on the Bureau. The Bureau adopts the policies of the Centre, recommends the nomination and the promotion of researchers and the appointment of regular members, advises the Director on the preparation of the budget and the Université de Montréal on the choice of the Director.

Two Committees Heading the CRM

Patrice Marcotte*Université de Montréal

Christiane RousseauUniversité de Montréal

Peter RussellMcGill University

Yvan Saint-AubinUniversité de Montréal

*Deputy directors are invited to meetings as observers.

65

Annual R

eport CR

M 2003-2004

Com

ités à la tête du CR

M

Walter CRAIG is Canada Research Chair of Math-ematical Analysis and its Ap-plications at the Department of Mathematics and Statis-tics of McMaster University. He received degrees from the University of California, Berkeley (B.A., 1977) and from the Courant Institute of Mathematical Sciences, New York University (M.Sc., 1979, and Ph.D., 1981) and has held positions at Brown University and Stanford University before joining McMaster. He is principally interested in linear and nonlinear partial differential equations, Hamiltonian dynami-cal systems, fl uid dynamics, quantum mechanics, and nonlinear functional analysis.

Peter GLYNN is Thomas W. Ford Professor in the School of Engineering at Stanford Univer-sity. He received his Ph.D in Op-erations Research from Stanford University in 1982. He is a Fellow of the Institute of Mathematical Statistics and his research interests focus on computational probabil-ity, queueing theory, statistical in-ference for stochastic processes, and stochastic modeling.

Mark HAIMAN is a Professor at the Department of Mathe-matics of the University of Cali-fornia, Berkeley. He received his degrees from the Massachu-setts Institute of Technology in Computer Science and Electri-cal Engineering (B.Sc., 1979) and in Mathematics (Ph.D., 1984). His research interests are in algebraic combinatorics, alge-braic geometry, representation theory, and lattice theory.

Nigel HITCHIN is Savilian Professor of Geometry at New College, Oxford University. He holds a Ph.D. degree in Mathematics (1972) from Wolfson Col-lege of Oxford University. He is princi-pally interested in differential and alge-braic geometry and its relationship with the equations of mathematical physics. Current projects include the areas of hy-perkähler geometry, special Lagrangian geometry and mirror symmetry, geomet-ric solutions of Painlevé equations, magnetic monopoles, vector bundles on algebraic curves, and the theory of gerbes.

Richard LOCKHART is a Professor at the Department of Statistics and Ac-tuarial Science of Simon Fraser Univer-sity. He received a B.Sc. in Mathematics from the University of British Columbia (1975) and degrees in Statistics from the University of California, Berkeley (M.A., 1976, Ph.D., 1979). He was President of the Statistical Society of Canada in 1996-1997. Much of his work is in the area of model assessment, generally in the form of goodness-of-fi t.

Mitchell LUSKIN is a Professor of Mathematics at the University of Minnesota, a Fellow of the Minne-sota Supercomputing Institute and a member of the graduate faculty of the Department of Aerospace Enginee-ring and Mechanics of the University of Minnesota. He holds degrees in Mathematics from Yale University (B.Sc., 1973) and the University of Chicago (M.Sc., 1976, Ph.D., 1977). His research interests include numerical analysis, scientific computing, applied mathematics, partial differential equations, computational materials science, and computational physics.

Scientifi c Advisory Commitee The Scientifi c Advisory Committee is constituted of distinguished researchers from Canada and abroad. Its members are either mathematicians or scientists with close ties to the mathematical sciences. The rector of the Université de Montréal and the Director of the CRM attend the meetings of the Scientifi c Advisory Committee. The Advisory Committee is informed periodically of the activities of the Centre, through the Director, and transmits any advice that it deems relevant to the Bu-reau de direction.

66

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ual R

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t CR

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2004

Ram MURTY est professeur titulaire de mathématiques et Queen’s Research Chair à l’Université Queen’s. Il est diplômé de MIT (Ph.D., 1980). Un spécialiste de la théorie des nom-bres algébrique et analytique, ses recherches portent sur la conjecture d’Artin, les courbes elliptiques, les formes modulaires, les formes automorphes, le programme de Langlands, les conjectures de Selberg, les méthodes de crible et la cryptographie.

Carl POMERANCE is a Professor at the Department of Mathematics of Dartmouth College. From 1999 to 2003, he was a member of the technical staff of Bell Labs-Lucent Technologies. He holds degrees from Brown University (B.A., 1966) and from Harvard University (M.A., 1970, Ph.D., 1972). A number theory special-ist, he has received numerous prizes and awards including the Levi L. Conant Prize of the American Mathematical So-ciety.

Peter B. SHALEN is a Professor at the Department Mathema-tics, Statistics and Computer Science at The University of Illinois at Chicago. He received his B.A. from Harvard College (1966) and his Ph.D. from Harvard University (1972). He also spent a year as an undergraduate at École Normale Supérieure in Paris. His main research interests are 3-dimensional topology, hyperbolic geometry, and geometric and combinatorial group theory.

Steven ZELDITCH is a Professor of Mathematics at Jo-hns Hopkins University. He received his Ph.D. from the University of California, Berkeley, in 1981. His research centers around applications of microlocal analysis to problems concerning: asymptotics of eigenfunctions/eigenvalues on Riemannian manifolds, statistical algebraic geometry, problems of mathematical physics ranging from quantum chaos to 2D Yang-Mills to string/M theory.

Alain Caillé Christiane RousseauChristian Léger

Alain Caillé, Vice-Principal (Research), Université de Montréal, Christian Léger, CRM Acting Director, and Christiane Rous-seau was President of the Canadian Mathematical Society from 2002-2004. are ex-offi cio members of the Advisory Committee.

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Personnel

Personnel 2003-2004

Christian Léger Director by interimTony Humphries Deputy Director, Scientific ProgramPatrice Marcotte Deputy Director, MITACSJean LeTourneux Deputy Director, PublicationsDiane Poulin Secretary

Administration

Vincent Masciotra Head of AdministrationMichèle Gilbert Administrative AssistantMuriel Pasqualetti Administrative AssistantGuillermo Martinez-Zalce Research Laboratories Administrative CoordinatorDiane Brulé-De-Filippis SecretaryJosée Simard Secretary

Scientific Activities

Louis Pelletier CoordinatorJosée Laferrière Assistant Coordinator

The Director’s Office

Suzette Paradis Communications Officer & Webmaster

Communications

Publications

André Montpetit TeX Expert (1/2 time)Louise Letendre Technician

Computer Services

Daniel Ouimet Systems AdministratorAndré Montpetit Office Systems Manager (1/2 time)

68

Ann

ual R

epor

t CR

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003-

2004

Sta

tem

ent o

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69

Annual R

eport CR

M 2003-2004

Statem

ent of revenue and expenditures

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gram

on

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The Centre de recherches mathématiques (CRM) was created in 1969 by the Université de Montréal through a special grant from the National Research Council of Canada. It became an NSERC national research centre in 1984. It is currently funded by NSERC (Natural Sciences and Engineering Research Council), by the Gov-ernment of Québec through the FQRNT (Fonds québécois de la recherche sur la nature et les technologies), by the Université de Montréal, as well as McGill, du Québec à Montréal, Concordia, Ottawa, Laval universities and by private donations. The mission of the CRM is to do research in mathematics and closely related disciplines and to provide leadership in the development of the mathematical sciences in Canada.

The CRM carries on its mission and national mandate in several ways:

• it organizes a series of scientific events each year, around a given theme (distinguished lecture series, workshops, conferences, summer schools, visitor programs, etc.);

• its general program provides funding for conferences and spe-cial events at the CRM and across the country;

• each year it invites, through the Aisenstadt Chair, one or more distinguished mathematicians, to give advanced courses as part of its thematic program;

• it awards four prizes yearly: the CRM-Fields Prize recognizing major contributions to mathematics, the Aisenstadt Prize given for outstanding work done by a young Canadian mathemati-cian, the CAP-CRM Prize for exceptional achievement in theo-retical and mathematical physics, and the CRM-SSC Prize for exceptional contributions to statistics in early career;

• it publishes technical reports and about ten books per year. Some of its collections are published jointly with the AMS and with Springer Verlag;

• it has an extensive postdoctoral fellowship program, with more than thirty postdoctoral fellows in place last year, funded either solely by the CRM or in partnership with other organizations;

• it informs the community of its activities through its newsletter, Bulletin du CRM, and its web site at www.CRM.UMontreal.CA;

• it participates, with the other two Canadian centres, in ground-breaking national initiatives. One example is the MITACS project (Mathematics of Information Technology and Com-plex Systems). Another example is the National Program Com-mittee, which provides funding for off-site research activities. Finally, the three institutes contribute financially to the devel-opment of the mathematical sciences in the Atlantic provinces through AARMS, and also participate in the National Program on Complex Data Structures jointly with the Canadian statisti-cal community.

This national mandate is complemented by, and indeed supported by, a long-standing vocation of promoting research in the math-ematical sciences in Québec. For instance,

• the CRM supports research through its eight research laborato-ries spanning most of the important areas of the mathematical sciences;

• it supports, through partnership agreements, a group of local researchers chosen mainly from departments of mathematics and statistics, but also computer science, physics, economics, engineering, etc.;

• it organizes series of regular seminars and lecture courses on dif-ferent areas of the mathematical sciences;

• it sponsors joint activities with the ISM (Institut des sciences mathématiques) including the weekly CRM/ISM colloquium, graduate courses offered by distinguished visitors and a program of postdoctoral fellowships;

• it works actively at developing contacts with industry. Its joint activities with liaison and research centres (CERCA, CIRANO and CRIM) and research centres doing applied research (CRT, GERAD and INRS-Télécommunications) led to the creation of the Network for Computing and Mathematical Modelling (ncm

2). NSERC and about twenty partners such as financial in-

stitutions, high-tech companies and government agencies fund this network.

The CRM fulfils its national mission by involving the largest possi-ble number of Canadian mathematicians in its scientific programs, both as participants and as organizers. It also supports many events taking place outside Montréal and the Province of Québec. It is recognized worldwide as one of the major institutes in the math-ematical sciences.

The director of the CRM is assisted by two managerial structures: the Bureau de direction and the Scientific Advisory Committee. The Advisory Committee is a group of internationally renowned mathematicians from Canada and abroad, who approve scientific programs and thematic years, choose recipients of the Aisenstadt Prize, participate in the selection of the CRM-Fields Prize, and suggest new scientific ventures to explore.

Mission of the CRM

70

Ann

ual R

epor

t CR

M 2

003-

2004

annual report 03-04 - centre de recherches mathématiques

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